Bonn Topology Group - Abstracts
General Information - Members - Activities - Topology Seminar
Talk
May 19th 2020
Julia Semikina (RFWU Bonn): Cut-and-paste invariants of manifolds via algebraic K-theory
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 (joint work with R. Hoekzema, M. Merling, L. Murray, and C. Rovi). 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 describe how the Euler characteristic, which is an example of a cut-and-paste invariant, fits into this new setup. Further we discuss what is conjecturally expected from the higher homotopy groups of the constructed spectrum and its potential connection to the classical notions such as Madsen-Tillmann spectra.
Back to seminar page
News
Bonn mathematics performs excellently again in QS ranking
Stefan Schwede is invited speaker at the ECM 2024 in Sevilla
Jessica Fintzen wins Cole Prize
Regula Krapf receives university teaching award
Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Grants for Mathematics students from Ukraine
Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Peter Scholze elected as Foreign Member of the Royal Society