### Bott periodicity in Algebra

Segal, G *(University of Oxford)*

Wednesday 03 April 2013, 13:30-14:30

Seminar Room 1, Newton Institute

#### Abstract

Topological K-theory was based on the Bott periodicity theorem, which made it possible to define K-groups in all degrees. Quillen's algebraic K-theory made use of a quite different principle. Nevertheless, Bott periodicity, seemingly so topological, has a variety of purely algebraic manifestations, which shed light on the sense in which an algebraically-defined space has a homotopy type.

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