Heegaard genus and property τ for hyperbolic 3-manifolds

D. D. Long; A. Lubotzky; A. W. Reid

doi:10.1112/jtopol/jtm010

Heegaard genus and property τ for hyperbolic 3-manifolds

D. D. Long^*
, A. Lubotzky^*
, A. W. Reid^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ. As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.

Original language	English
Pages (from-to)	152-158
Number of pages	7
Journal	Journal of Topology
Volume	1
Issue number	1
DOIs	https://doi.org/10.1112/jtopol/jtm010
State	Published - Jan 2008

Bibliographical note

Publisher Copyright:
© 2007 London Mathematical Society.

Access to Document

10.1112/jtopol/jtm010

Cite this

@article{7926d4b6777f47a9a82721a57e2e2171,

title = "Heegaard genus and property τ for hyperbolic 3-manifolds",

abstract = "We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ. As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.",

author = "Long, \{D. D.\} and A. Lubotzky and Reid, \{A. W.\}",

note = "Publisher Copyright: {\textcopyright} 2007 London Mathematical Society.",

year = "2008",

month = jan,

doi = "10.1112/jtopol/jtm010",

language = "אנגלית",

volume = "1",

pages = "152--158",

journal = "Journal of Topology",

issn = "1753-8416",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Heegaard genus and property τ for hyperbolic 3-manifolds

AU - Long, D. D.

AU - Lubotzky, A.

AU - Reid, A. W.

PY - 2008/1

Y1 - 2008/1

N2 - We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ. As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.

AB - We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ. As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.

UR - https://www.scopus.com/pages/publications/44449147282

U2 - 10.1112/jtopol/jtm010

DO - 10.1112/jtopol/jtm010

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:44449147282

SN - 1753-8416

VL - 1

SP - 152

EP - 158

JO - Journal of Topology

JF - Journal of Topology

IS - 1

ER -

Heegaard genus and property τ for hyperbolic 3-manifolds

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this