Séminaire d'algèbre et de géométrie du 28-04-2025
Exposé de Julia Semikina
Le 28-04-2025 à 14:00, en P108 et en ligne.Cut-and-paste K-theory of manifolds and cobordisms
Résumé
The generalized Hilbert’s third problem asks about the invariants preserved under the scissors congruence operation: given a polytope P in Rn, one can cut P into a finite number of smaller polytopes and reassemble these to form Q. Kreck, Neumann and Ossa introduced and studied an analogous notion of cut-and-paste relation for manifolds called the SK-equivalence (“schneiden und kleben” is German for “cut and paste”). In this talk I will explain the construction that will allow us to speak about the “K-theory of manifolds” spectrum. The zeroth homotopy group of the constructed spectrum recovers the classical groups SKn. I will show how to relate the spectrum to the algebraic K-theory of integers, and how this leads to the Euler characteristic and the Kervaire semicharacteristic when restricted to the lower homotopy groups. Further I will describe the connection of our spectrum with the cobordism category.