| Résume | Après-midi de Topologie
Organisée par Christian Ausoni (LAGA), Geoffroy Horel (LAGA), Muriel Livernet (IMJ-PRG), Najib Idrissi (IMJ-PRG).
14h-15h : Mikala Janssen : Partial and unstable algebraic K-theory
We compare Yuan's partial algebraic K-theory with the models for unstable algebraic K-theory given by the reductive Borel-Serre categories. Partial algebraic K-theory is a "non-group completed" version of algebraic K-theory defined in terms of a universal property whereas the reductive Borel-Serre categories are hands-on 1-categories that assemble to a monoidal category. It turns out that they are equivalent as E_1-spaces.This is work in progress, joint with Dustin Clausen.
15h15-16h15 : Erik Lindell : Stable cohomology of \(\mathrm{Aut}(F_n)\) and the IA-automorphism group
The automorphism group of the free group \(F_n\) is an object that for a long time has been of interest in group theory and in low-dimensional topology, where it appears as a kind of mapping class group of a finite graph. In the two recent decades, a lot of progress has been made in understanding the cohomology of this group. In particular, there have been several results about the stable cohomology, i.e. the part where n is sufficiently large compared to the cohomological degree, where it becomes independent of n. In this talk, I will describe recent results about the stable cohomology with certain “twisted” coefficients, and work-in-progress about how it can be applied to study the cohomology of the IA-automorphism group, i.e. the subgroup of automorphisms acting trivially on the abelianization of \(F_n\). This group is analogous to the Torelli subgroup of the mapping class group of a surface and very little is generally known about its cohomology.
16h30-17h30 : Félix Loubaton : L'univalence lax pour les \((\infty,\omega)\)-catégories
Dans cette présentation, je formulerai l'univalence lax pour les \((\infty,\omega)\)-catégories. J'expliquerai ensuite comment ce résultat nous permet d'exprimer un lien fort entre la construction de Grothendieck pour les \((\infty,\omega)\)-catégories et les lax-colimites. |
