Quasihomomorphisms to real algebraic groups
Group Theory
2026-03-04 v2
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.
Cite
@article{arxiv.2601.22411,
title = {Quasihomomorphisms to real algebraic groups},
author = {Sami Douba and Francesco Fournier-Facio and Sam Hughes and Simon Machado},
journal= {arXiv preprint arXiv:2601.22411},
year = {2026}
}
Comments
17 pages. v2: Minor changes to accommodate simple targets with nontrivial finite center