A Quillen Stability Criterion for Bounded Cohomology
Carlos De la Cruz Mengual, Tobias Hartnick
TL;DR
This paper extends Quillen's homological stability criterion to continuous bounded cohomology, enabling new stability results for classical groups, with implications for algebraic topology and group theory.
Contribution
It introduces a novel stability criterion for bounded cohomology based on Quillen's approach, applicable to a broad class of classical groups.
Findings
New stability results for classical groups' bounded cohomology
Extension of Quillen's criterion to bounded cohomology
Framework for future stability investigations
Abstract
We provide a version of Quillen's homological stability criterion for continuous bounded cohomology. This criterion is exploited in the companion paper (arXiv:2201.03879) in order to derive new bounded cohomological stability results for various families of classical groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Operator Algebra Research