Norm-controlled cohomology of transformation groups

We generalize the result of Brandenbursky and Marcinkowski for the bounded cohomology of transformation groups to infinite volume case. To state the result, we introduce the notion of norm controlled cohomology as a generalization of bounded cohomology. This cohomology theory also provides a framewo...

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Bibliographic Details
Published in:arXiv.org 2023-02
Main Author: Kimura, Mitsuaki
Format: Article
Language:English
Subjects:
Homology
Online Access:Get full text
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Summary:We generalize the result of Brandenbursky and Marcinkowski for the bounded cohomology of transformation groups to infinite volume case. To state the result, we introduce the notion of norm controlled cohomology as a generalization of bounded cohomology. This cohomology theory also provides a framework for relative quasimorphisms.
ISSN:2331-8422