Seminar: Topology of character varieties of abelian groups

Speaker: Carlos Florentino (IST, Lisbon)

2012.09.20 | Christine Dilling

Date Wed 21 Nov
Time 16:00 17:00
Location Aud. D3 (1531-215)

Abstract

The description of the space of commuting elements in a compact Lie group is an interesting algebro-geometric problem with applications in Mathematical Physics. When the Lie group is complex reductive, this space is the character variety of a free abelian group. Let K be a compact Lie group (not necessarily connected) and G be its complexi?cation. We will consider, more generally, an arbitrary finitely generated abelian group A, and show that the conjugation orbit space Hom(A,K)/K is a strong deformation retract of the caracter variety Hom(A,G)//G. As a Corollary, in the case when G is connected and semisimple, we obtain necessary and sufficient conditions for Hom(A,G)//G to be irreducible.

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