Norm-controlled cohomology of transformation groups
Mitsuaki Kimura
TL;DR
This paper introduces norm-controlled cohomology, extending bounded cohomology to infinite volume transformation groups, and offers a framework for relative quasimorphisms, broadening the scope of cohomological analysis.
Contribution
It generalizes bounded cohomology to infinite volume cases via norm-controlled cohomology, enabling new analysis of transformation groups.
Findings
Generalization of bounded cohomology to infinite volume groups
Introduction of norm-controlled cohomology framework
Application to relative quasimorphisms
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory