11-14 octobre 2016
Fuseau horaire Europe/Paris

The loop space of a p-local group

13 oct. 2016 à 11:40
Amphi Figlarz ()

Amphi Figlarz

Invited speaker Topologie algébrique et applications


Prof. Ran Levi


The homotopy type of the loop space on the p-complete classifying space of a finite group was studied by myself and a few other researchers since the early 90s. The homology of such loop spaces is of particular interest from the homotopy theoretic point of view, as it exhibits a rather rigid behaviour, yet not very well understood. From the algebraic point of view, works of Benson-Greenlees-Iyengar suggest the loop space homology of p-completed classifying spaces provides interesting examples of much more general phenomena. In his 2009 paper "An algebraic model for chains on $\Omega BG^\wedge_p$", Benson showed that the homology can be defined purely algebraically through what he named a "squeezed resolution" for the group in question. The theory of p-local finite and compact groups allows one to study homotopy theoretic and algebraic properties of p-completed classifying spaces in a very general context, and where a genuine group is not necessarily available. Thus the question that arises naturally is whether one can construct an analog of a squeezed resolution for p-local groups. The answer to this question turns out to be positive in a more general sense. In an ongoing project with Broto and Oliver we show that for any small category $\mathcal{C}$ satisfying certain conditions, the homology of the loop space of its p-completed nerve can be understood algebraically by means of a squeezed resolution. In this talk I will present the construction of squeezed resolutions in this context and discuss some of their properties. I will also relate this to a number of interesting homotopy theoretic questions.

Auteur principal

Prof. Ran Levi (Aberdeen)

Documents de présentation

Aucun document.
Your browser is out of date!

Update your browser to view this website correctly. Update my browser now