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 :
“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 :
“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 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},
}
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},
}
