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UBC Theses and Dissertations
The topology of representation varieties Bergeron, Maxime Octave
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 ⊂ G be a maximal compact subgroup. Given a finitely generated nilpotent group Γ, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) endowed with the compact-open topology. 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.
Item Metadata
| Title |
The topology of representation varieties
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2016
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| Description |
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 ⊂ G be a maximal compact subgroup. Given a finitely generated nilpotent group Γ, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) endowed with the compact-open topology. 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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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2016-08-11
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0307464
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2016-09
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International