Bounded cohomology of transformation groups

Michael Brandenbursky; Michał Marcinkowski

doi:10.1007/s00208-021-02266-8

Bounded cohomology of transformation groups

Michael Brandenbursky
, Michał Marcinkowski

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

Let M be a complete connected Riemannian manifold of finite volume. We present a new method of constructing classes in bounded cohomology of transformation groups such as Homeo (M, μ) , Diff (M, vol) and Symp (M, ω). As an application we show that for many manifolds (in particular for hyperbolic surfaces) the third bounded cohomology of these groups is infinite dimensional.

Original language	English
Pages (from-to)	1181-1197
Number of pages	17
Journal	Mathematische Annalen
Volume	382
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02266-8
State	Published - 1 Apr 2022

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-021-02266-8

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title = "Bounded cohomology of transformation groups",

abstract = "Let M be a complete connected Riemannian manifold of finite volume. We present a new method of constructing classes in bounded cohomology of transformation groups such as Homeo (M, μ) , Diff (M, vol) and Symp (M, ω). As an application we show that for many manifolds (in particular for hyperbolic surfaces) the third bounded cohomology of these groups is infinite dimensional.",

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AB - Let M be a complete connected Riemannian manifold of finite volume. We present a new method of constructing classes in bounded cohomology of transformation groups such as Homeo (M, μ) , Diff (M, vol) and Symp (M, ω). As an application we show that for many manifolds (in particular for hyperbolic surfaces) the third bounded cohomology of these groups is infinite dimensional.

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U2 - 10.1007/s00208-021-02266-8

DO - 10.1007/s00208-021-02266-8

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SP - 1181

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JO - Mathematische Annalen

JF - Mathematische Annalen

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Bounded cohomology of transformation groups

Abstract

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