(Ir)regular singularities and Quantum Field Theory

PUBLICATIONS

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Character varieties and holomorphic bundles

Flawed groups and the topology of character varieties

Author(s)

Carlos Florentino,
Sean Lawton

Topic

Character varieties and holomorphic bundles

Abstract

A finitely presented group F is called flawed if Hom(F,G)//G deformation retracts onto its subspace Hom(F,K)/K for reductive affine algebraic groups G and maximal compact subgroups K in G. After discussing generalities concerning flawed groups, we show that all finitely generated groups isomorphic to a free product of nilpotent groups are flawed. This unifies and generalizes all previously known classes of flawed groups. We also provide further evidence for the authors’ conjecture that RAAGs (with torsion) are flawed. Lastly, we show direct products between finite groups and some flawed group are also flawed. These latter two theorems enlarge the known class of flawed groups.

Year

2022

Reference

Florentino, Carlos, and Sean Lawton. “Flawed groups and the topology of character varieties.” arXiv:2012.08481

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