Equivariant algebraic K-theory for ample groupoids

Dev Mukherjee (University of Oxford)

Thursday 13th November 15:00-16:00
Maths 311B

Abstract

We describe a general strategy to define and study (non-C*-algebraic) bivariant K-theories by forcing desired properties via successive Dwyer-Kan localisations of suitable categories of algebras. This approach allows for the possibility to arrive at presentable, stable infinity categorical refinements of bivariant theories such as Cuntz-Meyer-Rosenberg's bivariant K-theory for bornological algebras, and Cortiñas-Thom's algebraic kk-theory. We apply this approach to define an equivariant KK-theory for ample groupoids. Finally, we discuss how assembly maps may be defined purely formally as localisations. 

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