IMSc Webinar

K-theory for analytic and topological stacks

Devarshi Mukherjee

University of Oxford

We define and study fundamental properties of localising invariants for analytic and topological stacks using Efimov's continuous K-theory. In the analytic setting, we associate to a derived (complex or rigid) analytic space, a dualisable category of nuclear sheaves. In the topological setting, we associate to an etale topological stack, a dualisable category of sheaves on the associated groupoid; for the quotient stack of a proper group action, this recovers the category of equivariant sheaves. I will then discuss applications of K-theory for (1) analytic stacks to Grothendieck Riemann-Roch Theorems, and, (2) for topological stacks to the Farrel-Jones conjecture.