Julia Semikina: Cut and paste invariants of manifolds via algebraic K-theory

In this talk I will explain the K-theoretic construction due to Campbell and Zakharevich and its application that will allow us to speak about the cut and paste spectrum of manifolds. The zeroth homotopy group of the constructed spectrum recovers the classical SK-groups ("schneiden und kleben" is German for "cut and paste") introduced by Kreck, Karras, Neumann and Ossa. I will explain how to relate the spectrum to the algebraic K-theory of integers, and how this leads to the classical invariants such as Euler characteristic and semicharacteristic when restricted to the lower homotopy groups.