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Noncommutative Borsuk-Ulam Theorems, Benjamin Passer

Arts & Sciences Electronic Theses and Dissertations

The Borsuk-Ulam theorem in algebraic topology shows that there are significant restrictions on how any topological sphere interacts with the antipodal action of reflection through the origin (which maps x to -x). For example, any map f from a sphere to itself which is continuous and odd (f(-x) = -f(x)) must be homotopically nontrivial. We consider various equivalent forms of the theorem in terms of the function algebras on spheres and examine which forms generalize to certain noncommutative Banach and C*-algebras with finite group actions.

Chapter 1 contains background material on C*-algebras, K-theory, and group actions. Next, in Chapter 2, …