PdD Candidate: Maxime Octave Bergeron
Mathematics, UBC

Mon 25 Jul 2016, 12:30pm
SPECIAL
Room 203, Graduate Student Centre, 6371 Crescent Road, UBC

Doctoral Exam: The Topology of Representation Varieties

Room 203, Graduate Student Centre, 6371 Crescent Road, UBC
Mon 25 Jul 2016, 12:30pm2:30pm
Details
Abstract: The goal of this thesis is to understand the topology of representation varieties. To be more precise, let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group Γ generated by r elements, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) with the natural topology induced from an embedding into Gr and Kr respectively. Our main result shows that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)//G onto the ordinary quotient Hom(Γ,K)/K. Using these deformations, we then describe the topology of these spaces.
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Latecomers will not be admitted.