Polynomially bounded cohomology and discrete groups
Crichton Ogle
TL;DR
This paper develops the foundational theory for polynomially bounded group cohomology and demonstrates an isomorphism with ordinary cohomology for specific classes of groups.
Contribution
It introduces the homological framework for polynomially bounded cohomology and proves an isomorphism with standard cohomology in certain cases.
Findings
Homological foundations for polynomially bounded cohomology established
Isomorphism between PH^*(G;Q) and H^*(G;Q) shown for specific groups
Provides tools for further study of bounded cohomology in group theory
Abstract
We establish the homological foundations for studying polynomially bounded group cohomology, and show that the natural map from PH^*(G;Q) to H^*(G;Q) is an isomorphism for a certain class of groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology