TOPOLOGICAL K-THEORY AND BOTT PERIODICITY

Author

Zachary Halladay

Date of Award

2019

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Kottke, Christopher

Area of Concentration

Mathematics

Abstract

In this thesis, we develop two equivalent formulations of topological K-theory and show how Ktheory forms the basis for an extraordinary cohomology theory as a consequence of Bott periodicity. We highlight the two different forms that Bott periodicity takes corresponding to the different formulations of K-theory and show how they are in fact compatible by an explicit homotopy detailed by Bott [7].

Recommended Citation

Halladay, Zachary, "TOPOLOGICAL K-THEORY AND BOTT PERIODICITY" (2019). Theses & ETDs. 5703.
https://digitalcommons.ncf.edu/theses_etds/5703