Topology of character varieties of Abelian groups

C. Florentino; S. Lawton

doi:10.1016/j.topol.2014.05.009

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arXiv · 1301.7616

Topology of character varieties of Abelian groups

C. Florentino·S. Lawton

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Abstract

Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation retract of the GIT quotient space Hom(A,G)//G. As a corollary, we determine necessary and sufficient conditions for the character variety Hom(A,G)//G to be irreducible when G is connected and semisimple. For a general connected reductive G, analogous conditions are found to be sufficient for irreducibility, when A is free abelian.

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BibTeX RIS

C. Florentino, S. Lawton. 2013-01-31. Topology of character varieties of Abelian groups. https://doi.org/10.1016/j.topol.2014.05.009

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