On the Farell-Jones conjecture for localizing invariants

Speaker:

Ulrich Bunke || GER

Zugehörigkeit:

University of Regensburg

Datum:

Mon, 27/06/2022 - 11:05 - 11:35

Parent event:

Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry [2]

This is a report on a joint project with D. Kasprowski and C. Winges. To every left-exact infinity category with a G-action and a finitary localizing invariant with target C we associate a functor from the orbit category of G to C. The Farrell-Jones conjecture asserts that this functor is equivalent to the left-Kan of its restriction to the subcategory of orbits whose stabilizers are vitually cyclic.
In the talk I will explain that the proofs of instances of this conjecture for special functors, e.g. algebraic K-theory can be adapted to provide a uniform argument for general functors as above, but the same class of groups.