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UBC Theses and Dissertations

Spaces of homomorphisms and commuting orthogonal matrices. Higuera Rojo, Galo


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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