Oberseminar Topologie: Iuliia Semikina (Münster): Cut-and-paste invariants of manifolds via algebraic K-theory

Monday, 07.12.2020 14:30 per ZOOM: Link to Zoom info

Mathematik und Informatik

Abstract: Recent work of Zakharevich and Campbell has focused on developing the K-theoretic machinery to study scissors congruence problems and applying these tools to the Grothendieck ring of varieties. In this talk we will discuss a new application of their framework to study the so called cut-and-paste invariants of manifolds. Namely, we will describe a K-theory spectrum, which recovers the classical groups SK_n ("schneiden und kleben" is German for "cut and paste") as its zeroth homotopy group. We will also explain how the Euler characteristic, which is an example of a cut-and-paste invariant, fits into this new setup. Further we will describe the connection of our spectrum to the classical Madsen-Tillmann spectrum MTSO(n). This is joint work with R. Hoekzema, M. Merling, L. Murray, and C. Rovi.


Angelegt am Monday, 30.11.2020 11:16 von juschult
Geändert am Sunday, 06.12.2020 19:44 von wuebbel
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