REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: The Atiyah-Bott-Shapiro construction is a classical connection between algebra and topology; roughly speaking, it is a way of mapping a module over a real or complex Clifford algebra to a class in the topological K-theory of a sphere. I will introduce a generalization of this construction, and I will show how one may use it to demonstrate precise senses in which various phenomena in commutative algebra are really manifestations of behaviors found in topology.