J. Hass and J. H. Rubinstein :
“One-sided closed geodesics on surfaces ,”
Mich. Math. J.
33 : 2
(1986 ),
pp. 155–168 .
MR
837574
Zbl
0614.53035
article

People
BibTeX
@article {key837574m,
AUTHOR = {Hass, Joel and Rubinstein, J. H.},
TITLE = {One-sided closed geodesics on surfaces},
JOURNAL = {Mich. Math. J.},
FJOURNAL = {Michigan Mathematical Journal},
VOLUME = {33},
NUMBER = {2},
YEAR = {1986},
PAGES = {155--168},
DOI = {10.1307/mmj/1029003345},
NOTE = {MR:837574. Zbl:0614.53035.},
ISSN = {0026-2285},
}
J. Hass, H. Rubinstein, and P. Scott :
“Covering spaces of 3-manifolds ,”
Bull. Am. Math. Soc., New Ser.
16 : 1
(January 1987 ),
pp. 117–119 .
MR
866028
Zbl
0624.57016
article

People
BibTeX
@article {key866028m,
AUTHOR = {Hass, Joel and Rubinstein, Hyam and
Scott, Peter},
TITLE = {Covering spaces of 3-manifolds},
JOURNAL = {Bull. Am. Math. Soc., New Ser.},
FJOURNAL = {Bulletin of the American Mathematical
Society (New Series)},
VOLUME = {16},
NUMBER = {1},
MONTH = {January},
YEAR = {1987},
PAGES = {117--119},
DOI = {10.1090/S0273-0979-1987-15481-4},
NOTE = {MR:866028. Zbl:0624.57016.},
ISSN = {0273-0979},
CODEN = {BAMOAD},
}
J. Hass, H. Rubinstein, and P. Scott :
“Compactifying coverings of closed 3-manifolds ,”
J. Differ. Geom.
30 : 3
(1989 ),
pp. 817–832 .
MR
1021374
Zbl
0693.57011
article

People
BibTeX
@article {key1021374m,
AUTHOR = {Hass, Joel and Rubinstein, Hyam and
Scott, Peter},
TITLE = {Compactifying coverings of closed 3-manifolds},
JOURNAL = {J. Differ. Geom.},
FJOURNAL = {Journal of Differential Geometry},
VOLUME = {30},
NUMBER = {3},
YEAR = {1989},
PAGES = {817--832},
URL = {http://projecteuclid.org/euclid.jdg/1214443831},
NOTE = {MR:1021374. Zbl:0693.57011.},
ISSN = {0022-040X},
CODEN = {JDGEAS},
}
J. Hass, J. T. Pitts, and J. H. Rubinstein :
“Existence of unstable minimal surfaces in manifolds with homology and applications to triply periodic minimal surfaces ,”
pp. 147–162
in
Differential geometry
(Los Angeles, 8–28 July 1990 ),
part 1: Partial differential equations on manifolds .
Edited by R. E. Green and S.-T. Yau .
Proceedings of Symposia in Pure Mathematics 54 .
American Mathematical Society (Providence, RI ),
1993 .
MR
1216582
Zbl
0798.53009
incollection

People
BibTeX
@incollection {key1216582m,
AUTHOR = {Hass, Joel and Pitts, Jon T. and Rubinstein,
J. H.},
TITLE = {Existence of unstable minimal surfaces
in manifolds with homology and applications
to triply periodic minimal surfaces},
BOOKTITLE = {Differential geometry},
EDITOR = {Green, Robert Everist and Yau, Shing-Tung},
VOLUME = {1: Partial differential equations on
manifolds},
SERIES = {Proceedings of Symposia in Pure Mathematics},
NUMBER = {54},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1993},
PAGES = {147--162},
NOTE = {(Los Angeles, 8--28 July 1990). MR:1216582.
Zbl:0798.53009.},
ISSN = {0082-0717},
ISBN = {9780821814949},
}
I. R. Aitchison and J. H. Rubinstein :
“Combinatorial Dehn surgery on cubed and Haken 3-manifolds ,”
pp. 1–21
in
Proceedings of the KirbyFest
(Berkeley, CA, 22–26 June 1998 ).
Edited by J. Hass and M. Scharlemann .
Geometry & Topology Monographs 2 .
International Press (Cambridge, MA ),
1999 .
Papers dedicated to Rob Kirby on the occasion of his 60th birthday.
MR
1734399
Zbl
0948.57016
ArXiv
9911072
incollection

Abstract
People
BibTeX

A combinatorial condition is obtained for when immersed or embedded incompressible surfaces in compact 3-manifolds with tori boundary components remain incompressible after Dehn surgery. A combinatorial characterisation of hierarchies is described. A new proof is given of the topological rigidity theorem of Hass and Scott for 3-manifolds containing immersed incompressible surfaces, as found in cubings of non-positive curvature.

@incollection {key1734399m,
AUTHOR = {Aitchison, I. R. and Rubinstein, J.
H.},
TITLE = {Combinatorial {D}ehn surgery on cubed
and {H}aken 3-manifolds},
BOOKTITLE = {Proceedings of the {K}irby{F}est},
EDITOR = {Hass, Joel and Scharlemann, Martin},
SERIES = {Geometry \& Topology Monographs},
NUMBER = {2},
PUBLISHER = {International Press},
ADDRESS = {Cambridge, MA},
YEAR = {1999},
PAGES = {1--21},
DOI = {10.2140/gtm.1999.2.1},
NOTE = {(Berkeley, CA, 22--26 June 1998). Papers
dedicated to Rob Kirby on the occasion
of his 60th birthday. ArXiv:9911072.
MR:1734399. Zbl:0948.57016.},
ISSN = {1464-8997},
ISBN = {9781571460868},
}
H. Rubinstein and M. Scharlemann :
“Genus two Heegaard splittings of orientable three-manifolds ,”
pp. 489–553
in
Proceedings of the KirbyFest
(Berkeley, CA, 22–26 June 1998 ).
Edited by J. Hass and M. Scharlemann .
Geometry & Topology Monographs 2 .
International Press (Cambridge, MA ),
1999 .
Papers dedicated to Rob Kirby on the occasion of his 60th birthday.
MR
1734422
Zbl
0962.57013
ArXiv
9712262
incollection

Abstract
People
BibTeX

It was shown by Bonahon–Otal and Hodgson–Rubinstein that any two genus-one Heegaard splittings of the same 3-manifold (typically a lens space) are isotopic. On the other hand, it was shown by Boileau, Collins and Zieschang that certain Seifert manifolds have distinct genus-two Heegaard splittings. In an earlier paper, we presented a technique for comparing Heegaard splittings of the same manifold and, using this technique, derived the uniqueness theorem for lens space splittings as a simple corollary. Here we use a similar technique to examine, in general, ways in which two non-isotopic genus-two Heegard splittings of the same 3-manifold compare, with a particular focus on how the corresponding hyperelliptic involutions are related

@incollection {key1734422m,
AUTHOR = {Rubinstein, Hyam and Scharlemann, Martin},
TITLE = {Genus two {H}eegaard splittings of orientable
three-manifolds},
BOOKTITLE = {Proceedings of the {K}irby{F}est},
EDITOR = {Hass, Joel and Scharlemann, Martin},
SERIES = {Geometry \& Topology Monographs},
NUMBER = {2},
PUBLISHER = {International Press},
ADDRESS = {Cambridge, MA},
YEAR = {1999},
PAGES = {489--553},
DOI = {10.2140/gtm.1999.2.489},
NOTE = {(Berkeley, CA, 22--26 June 1998). Papers
dedicated to Rob Kirby on the occasion
of his 60th birthday. ArXiv:9712262.
MR:1734422. Zbl:0962.57013.},
ISSN = {1464-8997},
ISBN = {9781571460868},
}
J. Hass, P. Norbury, and J. H. Rubinstein :
“Minimal spheres of arbitrarily high Morse index ,”
Commun. Anal. Geom.
11 : 3
(2003 ),
pp. 425–439 .
MR
2015753
Zbl
1104.53055
ArXiv
0206286
article

Abstract
People
BibTeX
@article {key2015753m,
AUTHOR = {Hass, Joel and Norbury, Paul and Rubinstein,
J. Hyam},
TITLE = {Minimal spheres of arbitrarily high
{M}orse index},
JOURNAL = {Commun. Anal. Geom.},
FJOURNAL = {Communications in Analysis and Geometry},
VOLUME = {11},
NUMBER = {3},
YEAR = {2003},
PAGES = {425--439},
URL = {http://intlpress.com/CAG/2003/11-3/CAG_11_425_439.pdf},
NOTE = {ArXiv:0206286. MR:2015753. Zbl:1104.53055.},
ISSN = {1019-8385},
}
J. Hass, J. H. Rubinstein, and A. Thompson :
“Knots and \( k \) -width ,”
Geom. Dedicata
143 : 1
(2009 ),
pp. 7–18 .
MR
2576289
Zbl
1189.57005
ArXiv
0604256
article

Abstract
People
BibTeX
@article {key2576289m,
AUTHOR = {Hass, Joel and Rubinstein, J. Hyam and
Thompson, Abigail},
TITLE = {Knots and \$k\$-width},
JOURNAL = {Geom. Dedicata},
FJOURNAL = {Geometriae Dedicata},
VOLUME = {143},
NUMBER = {1},
YEAR = {2009},
PAGES = {7--18},
DOI = {10.1007/s10711-009-9368-z},
NOTE = {ArXiv:0604256. MR:2576289. Zbl:1189.57005.},
ISSN = {0046-5755},
CODEN = {GEMDAT},
}