D. Eisenbud, U. Hirsch, and W. Neumann :
“Transverse foliations of Seifert bundles and self-homeomorphism of the circle Comment. Math. Helv.
56 : 4
(1981 ),
pp. 638–660 .
MR
656217 Zbl
0516.57015 article
Abstract
People
BibTeX
@article {key656217m,
AUTHOR = {Eisenbud, David and Hirsch, Ulrich and
Neumann, Walter},
TITLE = {Transverse foliations of {S}eifert bundles
and self-homeomorphism of the circle},
JOURNAL = {Comment. Math. Helv.},
FJOURNAL = {Commentarii Mathematici Helvetici},
VOLUME = {56},
NUMBER = {4},
YEAR = {1981},
PAGES = {638--660},
DOI = {10.1007/BF02566232},
NOTE = {MR:656217. Zbl:0516.57015.},
ISSN = {0010-2571},
}
M. Jankins and W. D. Neumann :
Lectures on Seifert manifolds .
Brandeis Lecture Notes 2 .
Brandeis University (Waltham, MA ),
1983 .
MR
741334 book
People
BibTeX
@book {key741334m,
AUTHOR = {Jankins, Mark and Neumann, Walter D.},
TITLE = {Lectures on {S}eifert manifolds},
SERIES = {Brandeis Lecture Notes},
NUMBER = {2},
PUBLISHER = {Brandeis University},
ADDRESS = {Waltham, MA},
YEAR = {1983},
PAGES = {i+111},
NOTE = {MR:741334.},
ISSN = {1052-9373},
}
W. D. Neumann and D. Zagier :
“Volumes of hyperbolic three-manifolds Topology
24 : 3
(1985 ),
pp. 307–332 .
MR
815482 Zbl
0589.57015 article
Abstract
People
BibTeX
By “hyperbolic 3-manifold” we will mean an orientable complete hyperbolic 3-manifold \( M \) of
finite volume. By Mostow rigidity the volume of \( M \) is a topological invariant, indeed a homotopy invariant, of the manifold \( M \) . There is in fact a purely topological definition of this invariant, due to Gromov. The set of all possible volumes of hyperbolic 3-manifolds is known to be a well-ordered subset of the real numbers and is of considerable interest (for number theoretic aspects see, for instance, [Borel 1981; Zagier 1986]) but remarkably little is known about it: the smallest element is not known even approximately, and it is not known whether any element of this set is rational or whether any element is irrational. For more details see Thurston’s Notes [1977]. In this paper we prove a result which, among other things, gives some metric or analytic information about the set of hyperbolic volumes.
@article {key815482m,
AUTHOR = {Neumann, Walter D. and Zagier, Don},
TITLE = {Volumes of hyperbolic three-manifolds},
JOURNAL = {Topology},
FJOURNAL = {Topology},
VOLUME = {24},
NUMBER = {3},
YEAR = {1985},
PAGES = {307--332},
DOI = {10.1016/0040-9383(85)90004-7},
NOTE = {MR:815482. Zbl:0589.57015.},
ISSN = {0040-9383},
}
R. Bieri, W. D. Neumann, and R. Strebel :
“A geometric invariant of discrete groups Invent. Math.
90 : 3
(1987 ),
pp. 451–477 .
MR
914846 Zbl
0642.57002 article
People
BibTeX
@article {key914846m,
AUTHOR = {Bieri, Robert and Neumann, Walter D.
and Strebel, Ralph},
TITLE = {A geometric invariant of discrete groups},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {90},
NUMBER = {3},
YEAR = {1987},
PAGES = {451--477},
DOI = {10.1007/BF01389175},
NOTE = {MR:914846. Zbl:0642.57002.},
ISSN = {0020-9910},
}
W. D. Neumann and A. W. Reid :
“Amalgamation and the invariant trace field of a Kleinian group Math. Proc. Cambridge Philos. Soc.
109 : 3
(1991 ),
pp. 509–515 .
MR
1094749 Zbl
0728.57009 article
People
BibTeX
@article {key1094749m,
AUTHOR = {Neumann, Walter D. and Reid, Alan W.},
TITLE = {Amalgamation and the invariant trace
field of a {K}leinian group},
JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
FJOURNAL = {Mathematical Proceedings of the Cambridge
Philosophical Society},
VOLUME = {109},
NUMBER = {3},
YEAR = {1991},
PAGES = {509--515},
DOI = {10.1017/S0305004100069942},
NOTE = {MR:1094749. Zbl:0728.57009.},
ISSN = {0305-0041},
}
Topology ’90: Papers from the research semester in low-dimensional topology held at Ohio State University Columbus, OH, February–June 1990 ).
Edited by B. Apanasov, W. D. Neumann, A. W. Reid, and L. Siebenmann .
Ohio State University Mathematical Research Institute Publications 1 .
de Gruyter (Berlin ),
1992 .
MR
1184397 Zbl
0747.00024 book
People
BibTeX
@book {key1184397m,
TITLE = {Topology '90: {P}apers from the research
semester in low-dimensional topology
held at {O}hio {S}tate {U}niversity},
EDITOR = {Apanasov, Boris and Neumann, Walter
D. and Reid, Alan W. and Siebenmann,
Laurent},
SERIES = {Ohio State University Mathematical Research
Institute Publications},
NUMBER = {1},
PUBLISHER = {de Gruyter},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {xii + 457},
DOI = {10.1515/9783110857726},
NOTE = {(Columbus, OH, February--June 1990).
MR:1184397. Zbl:0747.00024.},
ISSN = {0942-0363},
ISBN = {9783110125986},
}
W. D. Neumann and A. W. Reid :
“Arithmetic of hyperbolic manifolds 273–310
in
Topology ’90: Papers from the research semester in low-dimensional topology held at Ohio State University
(Columbus, OH, February–June 1990 ).
Edited by B. Apanasov, W. D. Neumann, A. W. Reid, and L. Siebenmann .
Ohio State University Mathematics Research Institute Publications 1 .
de Gruyter (Berlin ),
1992 .
MR
1184416 Zbl
0777.57007 incollection
People
BibTeX
@incollection {key1184416m,
AUTHOR = {Neumann, Walter D. and Reid, Alan W.},
TITLE = {Arithmetic of hyperbolic manifolds},
BOOKTITLE = {Topology '90: {P}apers from the research
semester in low-dimensional topology
held at {O}hio {S}tate {U}niversity},
EDITOR = {Apanasov, Boris and Neumann, Walter
D. and Reid, Alan W. and Siebenmann,
Laurent},
SERIES = {Ohio State University Mathematics Research
Institute Publications},
NUMBER = {1},
PUBLISHER = {de Gruyter},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {273--310},
URL = {https://www.degruyter.com/document/doi/10.1515/9783110857726/pdf#page=285},
NOTE = {(Columbus, OH, February--June 1990).
MR:1184416. Zbl:0777.57007.},
ISSN = {0942-0363},
ISBN = {9783110125986},
}
W. D. Neumann and A. W. Reid :
“Notes on Adams’ small volume orbifolds 311–314
in
Topology ’90: Papers from the research semester in low-dimensional topology held at Ohio State University
(Columbus, OH, February–June 1990 ).
Edited by B. Apanasov, W. D. Neumann, A. W. Reid, and L. Siebenmann .
Ohio State University Mathematics Research Institute Publications 1 .
de Gruyter (Berlin ),
1992 .
MR
1184417 Zbl
0773.57009 incollection
Abstract
People
BibTeX
In [1992] Colin Adams shows there we just six non-compact orientable hyperbolic 3-orbifolds of volume less than \( v_0/4 \) , where \( v_0 = 1.01494146\dots \) is the volume of a regular ideal tetrahedron in \( \mathbb{H}^3 \) . We give various descriptions of them and their fundamental groups. In particular, we will see that they are all arithmetic, and we give explicit commensurabilities between some of them. Their fundamental groups can be described as symmetry groups of tesselations, so we will introduce terminology for this. Many of them am also “tetrahedral groups,” so we introduce notation for these too.
These orbifolds show that “cusp density” is not a commensurability invariant of one-cusped orbifolds, answering a question that has been asked by several people. As we discuss in Sect. 3, cusp density is a commensurability invariant for non-arithmetic one-cusped orbifolds.
@incollection {key1184417m,
AUTHOR = {Neumann, Walter D. and Reid, Alan W.},
TITLE = {Notes on {A}dams' small volume orbifolds},
BOOKTITLE = {Topology '90: {P}apers from the research
semester in low-dimensional topology
held at {O}hio {S}tate {U}niversity},
EDITOR = {Apanasov, Boris and Neumann, Walter
D. and Reid, Alan W. and Siebenmann,
Laurent},
SERIES = {Ohio State University Mathematics Research
Institute Publications},
NUMBER = {1},
PUBLISHER = {de Gruyter},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {311--314},
URL = {https://www.degruyter.com/document/doi/10.1515/9783110857726/pdf#page=323},
NOTE = {(Columbus, OH, February--June 1990).
MR:1184417. Zbl:0773.57009.},
ISSN = {0942-0363},
ISBN = {9783110125986},
}
W. D. Neumann :
“Combinatorics of triangulations and the Chern–Simons invariant for hyperbolic 3-manifolds 243–271
in
Topology ’90: Papers from the research semester in low-dimensional topology held at Ohio State University
(Columbus, OH, February–June 1990 ).
Edited by B. Apanasov, W. D. Neumann, A. W. Reid, and L. Siebenmann .
Ohio State University Mathematics Research Institute Publications 1 .
de Gruyter (Berlin ),
1992 .
MR
1184415 Zbl
0768.57006 incollection
Abstract
People
BibTeX
In this paper we prove some results on combinatorics of triangulations of 3-dimensional pseudo-manifolds, improving on results of [Neumann and Zagier 1985], and apply them to obtain a simplicial formula for the Chern–Simons invariant of an ideally triangulated hyperbolic 3-manifold. Combining this with [Meyerhoff and Neumann 1991] gives a simplicial formula for the \( \eta \) invariant also.
@incollection {key1184415m,
AUTHOR = {Neumann, Walter D.},
TITLE = {Combinatorics of triangulations and
the {C}hern--{S}imons invariant for
hyperbolic 3-manifolds},
BOOKTITLE = {Topology '90: {P}apers from the research
semester in low-dimensional topology
held at {O}hio {S}tate {U}niversity},
EDITOR = {Apanasov, Boris and Neumann, Walter
D. and Reid, Alan W. and Siebenmann,
Laurent},
SERIES = {Ohio State University Mathematics Research
Institute Publications},
NUMBER = {1},
PUBLISHER = {de Gruyter},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {243--271},
URL = {https://www.degruyter.com/document/doi/10.1515/9783110857726/pdf#page=255},
NOTE = {(Columbus, OH, February--June 1990).
MR:1184415. Zbl:0768.57006.},
ISSN = {0942-0363},
ISBN = {9783110125986},
}
W. D. Neumann and A. W. Reid :
“Rigidity of cusps in deformations of hyperbolic 3-orbifolds Math. Ann.
295 : 2
(1993 ),
pp. 223–237 .
MR
1202390 Zbl
0813.57013 article
People
BibTeX
@article {key1202390m,
AUTHOR = {Neumann, Walter D. and Reid, Alan W.},
TITLE = {Rigidity of cusps in deformations of
hyperbolic 3-orbifolds},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {295},
NUMBER = {2},
YEAR = {1993},
PAGES = {223--237},
DOI = {10.1007/BF01444885},
NOTE = {MR:1202390. Zbl:0813.57013.},
ISSN = {0025-5831},
}
W. D. Neumann and J. Yang :
“Rationality problems for \( K \) -theory and Chern–Simons invariants of hyperbolic 3-manifolds ,”
Enseign. Math. (2)
41 : 3–4
(1995 ),
pp. 281–296 .
MR
1365848 Zbl
0861.57022 article
Abstract
People
BibTeX
This paper makes certain observations regarding some conjectures of Milnor and Ramakrishnan in hyperbolic geometry and algebraic \( K \) -theory. As a consequence of our observations, we obtain new results and conjectures regarding the rationality and irrationality of Chern–Simons invariants of hyperbolic 3-manifolds.
@article {key1365848m,
AUTHOR = {Neumann, Walter D. and Yang, Jun},
TITLE = {Rationality problems for \$K\$-theory
and {C}hern--{S}imons invariants of
hyperbolic 3-manifolds},
JOURNAL = {Enseign. Math. (2)},
FJOURNAL = {L'Enseignement Math\'ematique. Revue
Internationale. 2e S\'erie},
VOLUME = {41},
NUMBER = {3--4},
YEAR = {1995},
PAGES = {281--296},
NOTE = {MR:1365848. Zbl:0861.57022.},
ISSN = {0013-8584},
}
W. D. Neumann :
“Commensurability and virtual fibration for graph manifolds Topology
36 : 2
(1997 ),
pp. 355–378 .
MR
1415593 Zbl
0872.57021 article
BibTeX
@article {key1415593m,
AUTHOR = {Neumann, Walter D.},
TITLE = {Commensurability and virtual fibration
for graph manifolds},
JOURNAL = {Topology},
FJOURNAL = {Topology},
VOLUME = {36},
NUMBER = {2},
YEAR = {1997},
PAGES = {355--378},
DOI = {10.1016/0040-9383(96)00014-6},
NOTE = {MR:1415593. Zbl:0872.57021.},
ISSN = {0040-9383},
}
W. D. Neumann :
“Hilbert’s 3rd problem and invariants of 3-manifolds 383–411
in
The Epstein birthday schrift .
Edited by I. Rivin, C. Rourke, and C. Series .
Geometry and Topology Monographs 1 .
Geometry and Topology Publishers (Coventry, UK ),
1998 .
Dedicated to David Epstein on the occasion of his 60th birthday.
MR
1668316 Zbl
0902.57013 ArXiv
math/9712226 incollection
Abstract
People
BibTeX
This paper is an expansion of my lecture for David Epstein’s birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This “logical progression” makes a good story but distorts history a bit: the ultimate aims of the characters in the story were often far from 3-manifold theory.
We start in section 1 with an exposition of the current state of Hilbert’s 3rd problem on scissors congruence for dimension 3. In section 2 we explain the relevance to 3-manifold theory and use this to motivate the Bloch group via a refined “orientation sensitive” version of scissors congruence. This is not the historical motivation for it, which was to study algebraic \( K \) -theory of \( \mathbb{C} \) . Some analogies involved in this “orientation sensitive” scissors congruence are not perfect and motivate a further refinement in Section 4. Section 5 ties together various threads and discusses some questions and conjectures.
@incollection {key1668316m,
AUTHOR = {Neumann, Walter D.},
TITLE = {Hilbert's 3rd problem and invariants
of 3-manifolds},
BOOKTITLE = {The {E}pstein birthday schrift},
EDITOR = {Rivin, Igor and Rourke, Colin and Series,
Caroline},
SERIES = {Geometry and Topology Monographs},
NUMBER = {1},
PUBLISHER = {Geometry and Topology Publishers},
ADDRESS = {Coventry, UK},
YEAR = {1998},
PAGES = {383--411},
DOI = {10.2140/gtm.1998.1.383},
NOTE = {Dedicated to David Epstein on the occasion
of his 60th birthday. ArXiv:math/9712226.
MR:1668316. Zbl:0902.57013.},
ISSN = {1464-8989},
}
W. D. Neumann and J. Yang :
“Bloch invariants of hyperbolic 3-manifolds Duke Math. J.
96 : 1
(1999 ),
pp. 29–59 .
MR
1663915 Zbl
0943.57008 ArXiv
math/9712224 article
Abstract
People
BibTeX
We define an invariant \( \beta(M) \) of a finite volume hyperbolic 3-manifold \( M \) in the Bloch group \( \mathscr{B}(\mathbb{C}) \) and show it is determined by the simplex parameters of any degree one ideal triangulation of \( M \) . We show \( \beta(M) \) lies in a subgroup of \( \mathscr{B}(\mathbb{C}) \) of finite \( \mathbb{Q} \) -rank determined by the invariant trace field of \( M \) . Moreover, the Chern–Simons invariant of \( M \) is determined modulo rationals by \( \beta(M) \) . This leads to a simplicial formula and rationality results for the Chern–Simons invariant which appear elsewhere.
Generalizations of \( \beta(M) \) are also described, as well as several interesting examples. An appendix describes a scissors congruence interpretation of \( \mathscr{B}(\mathbb{C}) \) .
@article {key1663915m,
AUTHOR = {Neumann, Walter D. and Yang, Jun},
TITLE = {Bloch invariants of hyperbolic 3-manifolds},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {96},
NUMBER = {1},
YEAR = {1999},
PAGES = {29--59},
DOI = {10.1215/S0012-7094-99-09602-3},
NOTE = {ArXiv:math/9712224. MR:1663915. Zbl:0943.57008.},
ISSN = {0012-7094},
}
D. Coulson, O. A. Goodman, C. D. Hodgson, and W. D. Neumann :
“Computing arithmetic invariants of 3-manifolds Experiment. Math.
9 : 1
(2000 ),
pp. 127–152 .
MR
1758805 Zbl
1002.57044 article
Abstract
People
BibTeX
Snap is a computer program for computing arithmetic invariants of hyperbolic 3-manifolds, built on Jeff Weeks’s SnapPea and the number theory package Pari. Its approach is to compute the hyperbolic structure to very high precision, and use th is to find an exact description of the structure. Then the correctness of the hyperbolic structure can be verified, and the arithmetic invariants of Neumann and Reid can be computed. Snap also computes high precision numerical invariants such as volume, Chern–Simons invariant, eta invariant, and the Borel regulator.
@article {key1758805m,
AUTHOR = {Coulson, David and Goodman, Oliver A.
and Hodgson, Craig D. and Neumann, Walter
D.},
TITLE = {Computing arithmetic invariants of 3-manifolds},
JOURNAL = {Experiment. Math.},
FJOURNAL = {Experimental Mathematics},
VOLUME = {9},
NUMBER = {1},
YEAR = {2000},
PAGES = {127--152},
DOI = {10.1080/10586458.2000.10504641},
URL = {http://projecteuclid.org/euclid.em/1046889596},
NOTE = {MR:1758805. Zbl:1002.57044.},
ISSN = {1058-6458},
}
W. D. Neumann :
“Extended Bloch group and the Cheeger–Chern–Simons class Geom. Topol.
8 : 1
(2004 ),
pp. 413–474 .
MR
2033484 Zbl
1053.57010 ArXiv
math/0307092 article
Abstract
BibTeX
We define an extended Bloch group and show it is naturally isomorphic to \( H_3(\textrm{PSL}(2,\mathbb{C})^{\delta};\mathbb{Z}) \) . Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger–Chern–Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volume and Chern–Simons invariant of hyperbolic 3-manifolds conjectured by Neumann and Zagier and proved by Yoshida, as well as effective formulae for the Chern–Simons invariant of a hyperbolic 3-manifold.
@article {key2033484m,
AUTHOR = {Neumann, Walter D.},
TITLE = {Extended {B}loch group and the {C}heeger--{C}hern--{S}imons
class},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry and Topology},
VOLUME = {8},
NUMBER = {1},
YEAR = {2004},
PAGES = {413--474},
DOI = {10.2140/gt.2004.8.413},
NOTE = {ArXiv:math/0307092. MR:2033484. Zbl:1053.57010.},
ISSN = {1465-3060},
}
C. J. Leininger, D. B. McReynolds, W. D. Neumann, and A. W. Reid :
“Length and eigenvalue equivalence Int. Math. Res. Not.
2007 : 24
(2007 ).
Article no. rnm135, 24 pp.
MR
2377017 Zbl
1158.53032 ArXiv
math/0606343 article
Abstract
People
BibTeX
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace–Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equivalent and primitive length equivalent Riemannian manifolds. For example, we show that every finite volume hyperbolic \( n \) -manifold has pairs of eigenvalue equivalent finite covers of arbitrarily large volume ratio. We also show the analogous result for primitive length equivalence.
@article {key2377017m,
AUTHOR = {Leininger, C. J. and McReynolds, D.
B. and Neumann, W. D. and Reid, A. W.},
TITLE = {Length and eigenvalue equivalence},
JOURNAL = {Int. Math. Res. Not.},
FJOURNAL = {International Mathematics Research Notices},
VOLUME = {2007},
NUMBER = {24},
YEAR = {2007},
DOI = {10.1093/imrn/rnm135},
NOTE = {Article no. rnm135, 24 pp. ArXiv:math/0606343.
MR:2377017. Zbl:1158.53032.},
ISSN = {1073-7928},
}
J. A. Behrstock and W. D. Neumann :
“Quasi-isometric classification of graph manifold groups Duke Math. J.
141 : 2
(February 2008 ),
pp. 217–240 .
MR
2376814 Zbl
1194.20045 ArXiv
math/0604042 article
Abstract
People
BibTeX
We show that the fundamental groups of any two closed irreducible nongeometric graph manifolds are quasi-isometric. We also classify the quasi-isometry types of fundamental groups of graph manifolds with boundary in terms of certain finite two-colored graphs. A corollary is the quasi-isometric classification of Artin groups whose presentation graphs are trees. In particular, any two right-angled Artin groups whose presentation graphs are trees of diameter greater than 2 are quasi-isometric; further, this quasi-isometry class does not include any other right-angled Artin groups.
@article {key2376814m,
AUTHOR = {Behrstock, Jason A. and Neumann, Walter
D.},
TITLE = {Quasi-isometric classification of graph
manifold groups},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {141},
NUMBER = {2},
MONTH = {February},
YEAR = {2008},
PAGES = {217--240},
DOI = {10.1215/S0012-7094-08-14121-3},
NOTE = {ArXiv:math/0604042. MR:2376814. Zbl:1194.20045.},
ISSN = {0012-7094},
}
J. A. Behrstock, T. Januszkiewicz, and W. D. Neumann :
“Commensurability and QI classification of free products of finitely generated abelian groups Proc. Am. Math. Soc.
137 : 3
(2009 ),
pp. 811–813 .
MR
2457418 Zbl
1183.20025 ArXiv
0712.0569 article
Abstract
People
BibTeX
@article {key2457418m,
AUTHOR = {Behrstock, Jason A. and Januszkiewicz,
Tadeusz and Neumann, Walter D.},
TITLE = {Commensurability and {QI} classification
of free products of finitely generated
abelian groups},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {137},
NUMBER = {3},
YEAR = {2009},
PAGES = {811--813},
DOI = {10.1090/S0002-9939-08-09559-2},
NOTE = {ArXiv:0712.0569. MR:2457418. Zbl:1183.20025.},
ISSN = {0002-9939},
}
W. D. Neumann :
“On Leighton’s graph covering theorem Groups Geom. Dyn.
4 : 4
(2010 ),
pp. 863–872 .
MR
2727669 Zbl
1210.05113 ArXiv
0906.2496 article
Abstract
BibTeX
We give short expositions of both Leighton’s proof and the Bass–Kulkarni proof of Leighton’s graph covering theorem, in the context of colored graphs. We discuss a further generalization, needed elsewhere, to “symmetry-restricted graphs”. We can prove it in some cases, for example, if the “graph of colors” is a tree, but we do not know if it is true in general. We show that Bass’s Conjugation Theorem, which is a tool in the Bass–Kulkarni approach, does hold in the symmetry-restricted context.
@article {key2727669m,
AUTHOR = {Neumann, Walter D.},
TITLE = {On {L}eighton's graph covering theorem},
JOURNAL = {Groups Geom. Dyn.},
FJOURNAL = {Groups, Geometry, and Dynamics},
VOLUME = {4},
NUMBER = {4},
YEAR = {2010},
PAGES = {863--872},
DOI = {10.4171/GGD/111},
NOTE = {ArXiv:0906.2496. MR:2727669. Zbl:1210.05113.},
ISSN = {1661-7207},
}
