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UBC Theses and Dissertations
Spaces of homomorphisms and commuting orthogonal matrices. Higuera Rojo, Galo
Abstract
In this work we study the space of group homomorphisms Hom (π,G) for special choices of π and G. In the first part of this thesis, we enumerate and describe the path components for the spaces of ordered commuting k-tuples of orthogonal and special orthogonal matrices respectively. This corresponds to choosing π = ℤk and G = O(n); SO(n). We also provide a lower bound on the number of components for the case G = Spin(n) for suffciently large n. In the second part, we describe the space Hom (Г,SU(2)), where Г is a group arising from a central extension of the form 0 → ℤr → Г → ℤk → 0. The description of this space is good enough that, using some known results, it allows us to compute its cohomology groups.
Item Metadata
| Title |
Spaces of homomorphisms and commuting orthogonal matrices.
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2014
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| Description |
In this work we study the space of group homomorphisms Hom (π,G) for
special choices of π and G. In the first part of this thesis, we enumerate and
describe the path components for the spaces of ordered commuting k-tuples
of orthogonal and special orthogonal matrices respectively. This corresponds
to choosing π = ℤk and G = O(n); SO(n). We also provide a lower bound
on the number of components for the case G = Spin(n) for suffciently large
n.
In the second part, we describe the space Hom (Г,SU(2)), where Г is a
group arising from a central extension of the form
0 → ℤr → Г → ℤk → 0.
The description of this space is good enough that, using some known results,
it allows us to compute its cohomology groups.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2014-04-23
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivs 2.5 Canada
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| DOI |
10.14288/1.0167318
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2014-05
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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-NoDerivs 2.5 Canada