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UBC Theses and Dissertations
Classifying spaces for topological Azumaya algebras Gant, William S.
Abstract
In this thesis, we study a family of smooth varieties, whose members are denoted B_n^r(C), that bears a similar relationship to topological Azumaya algebras as the Grassmannians G_{n,r}(C) do to complex vector bundles. Specifically, we will show that the varieties B_n^r(C) form homotopical approximations to the classifying space BPGL_n(C). The varieties B_n^r(C) are obtained by first considering the variety of r-tuples of nxn complex matrices that generate the matrix algebra Mat_n(C), and then taking the quotient by an evidently free PGL_n(C)-action. The focus of this thesis is a computation of the singular cohomology groups of B_n^r(C) when n=2. We will show how these cohomological computations have applications in bounding the minimal number of generating sections of a topological Azumaya algebra over a paracompact space.
Item Metadata
Title |
Classifying spaces for topological Azumaya algebras
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2020
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Description |
In this thesis, we study a family of smooth varieties, whose members are denoted B_n^r(C), that bears a similar relationship to topological Azumaya algebras as the Grassmannians G_{n,r}(C) do to complex vector bundles. Specifically, we will show that the varieties B_n^r(C) form homotopical approximations to the classifying space BPGL_n(C). The varieties B_n^r(C) are obtained by first considering the variety of r-tuples of nxn complex matrices that generate the matrix algebra Mat_n(C), and then taking the quotient by an evidently free PGL_n(C)-action. The focus of this thesis is a computation of the singular cohomology groups of B_n^r(C) when n=2. We will show how these cohomological computations have applications in bounding the minimal number of generating sections of a topological Azumaya algebra over a paracompact space.
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Language |
eng
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Date Available |
2020-08-24
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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 |
10.14288/1.0392923
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2020-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International