Cohomology of deformations

Uri Bader; Piotr W. Nowak

doi:https://doi.org/10.1142/S1793525315500041

Cohomology of deformations

Uri Bader, Piotr W. Nowak

Mathematics

Technion - Israel Institute of Technology

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

Abstract

In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.

Original language	English
Pages (from-to)	81-104
Number of pages	24
Journal	Journal of Topology and Analysis
Volume	7
Issue number	1
DOIs	https://doi.org/10.1142/S1793525315500041
State	Published - 23 Mar 2015

Keywords

Banach modules
Cohomology
deformations of representations

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Access to Document

https://doi.org/10.1142/S1793525315500041

Cite this

@article{3227eb67b2964ac087632eb466f1d3f5,

title = "Cohomology of deformations",

abstract = "In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.",

keywords = "Banach modules, Cohomology, deformations of representations",

author = "Uri Bader and Nowak, {Piotr W.}",

note = "Publisher Copyright: {\textcopyright} 2015 World Scientific Publishing Company.",

year = "2015",

month = mar,

day = "23",

doi = "https://doi.org/10.1142/S1793525315500041",

language = "الإنجليزيّة",

volume = "7",

pages = "81--104",

journal = "Journal of Topology and Analysis",

issn = "1793-5253",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "1",

}

TY - JOUR

T1 - Cohomology of deformations

AU - Bader, Uri

AU - Nowak, Piotr W.

PY - 2015/3/23

Y1 - 2015/3/23

N2 - In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.

AB - In this paper we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As applications we obtain deformation theorems for fixed point properties on Banach spaces. In particular, our results yield fixed point theorems for affine actions in which the linear part is not uniformly bounded. Our proofs are effective and allow for quantitative estimates.

KW - Banach modules

KW - Cohomology

KW - deformations of representations

UR - http://www.scopus.com/inward/record.url?scp=84942113079&partnerID=8YFLogxK

U2 - https://doi.org/10.1142/S1793525315500041

DO - https://doi.org/10.1142/S1793525315500041

M3 - مقالة

SN - 1793-5253

VL - 7

SP - 81

EP - 104

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 1

ER -

Cohomology of deformations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this