Quasihomomorphisms to real algebraic groups

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.