Quasihomomorphisms to real algebraic groups
Sami Douba, Francesco Fournier-Facio, Sam Hughes, Simon Machado

TL;DR
This paper extends the concept of quasihomomorphisms to real algebraic groups, proving a rigidity theorem that generalizes previous results for discrete groups, and clarifies their structure.
Contribution
It introduces a rigidity theorem for quasihomomorphisms into real algebraic groups, generalizing prior results from discrete groups.
Findings
Rigidity theorem for quasihomomorphisms into real algebraic groups
Extension of Fujiwara and Kapovich's results to continuous groups
Structural description of quasihomomorphisms in the new setting
Abstract
A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be built from homomorphisms and sections of bounded central extensions. We study quasihomomorphisms with values in real linear algebraic groups, and prove an analogous rigidity theorem.
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Taxonomy
TopicsGeometric and Algebraic Topology · Analytic and geometric function theory · Homotopy and Cohomology in Algebraic Topology
