Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

Izhar Oppenheim

doi:10.4171/GGD/306

Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

Izhar Oppenheim

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

10 Scopus citations

Abstract

We extend Ballmann and ͆wiatkowski's work on cohomology of groups acting on simplicial complexes and provide further vanishing results of cohomologies and of property (T). In particular, we give a new criterion for property (T) for groups acting on an n-dimensional simplicial complex.

Original language	English
Pages (from-to)	67-101
Number of pages	35
Journal	Groups, Geometry, and Dynamics
Volume	9
Issue number	1
DOIs	https://doi.org/10.4171/GGD/306
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

Continuous cohomology
Garland's method
Graph Laplacian
Kazhdan property (T)
Simplicial complexes

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/306

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title = "Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes",

abstract = "We extend Ballmann and ͆wiatkowski's work on cohomology of groups acting on simplicial complexes and provide further vanishing results of cohomologies and of property (T). In particular, we give a new criterion for property (T) for groups acting on an n-dimensional simplicial complex.",

keywords = "Continuous cohomology, Garland's method, Graph Laplacian, Kazhdan property (T), Simplicial complexes",

author = "Izhar Oppenheim",

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

year = "2015",

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doi = "10.4171/GGD/306",

language = "English",

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AU - Oppenheim, Izhar

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N2 - We extend Ballmann and ͆wiatkowski's work on cohomology of groups acting on simplicial complexes and provide further vanishing results of cohomologies and of property (T). In particular, we give a new criterion for property (T) for groups acting on an n-dimensional simplicial complex.

AB - We extend Ballmann and ͆wiatkowski's work on cohomology of groups acting on simplicial complexes and provide further vanishing results of cohomologies and of property (T). In particular, we give a new criterion for property (T) for groups acting on an n-dimensional simplicial complex.

KW - Continuous cohomology

KW - Garland's method

KW - Graph Laplacian

KW - Kazhdan property (T)

KW - Simplicial complexes

UR - https://www.scopus.com/pages/publications/84928677195

U2 - 10.4171/GGD/306

DO - 10.4171/GGD/306

M3 - Article

AN - SCOPUS:84928677195

SN - 1661-7207

VL - 9

SP - 67

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JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 1

ER -

Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

Abstract

Keywords

ASJC Scopus subject areas

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