11-14 octobre 2016
Fuseau horaire Europe/Paris

A small projective resolution of complex K-theory

12 oct. 2016 à 11:40
50m
Amphi Lavoisier ()

Amphi Lavoisier

Invited speaker Topologie algébrique et applications

Orateur

Prof. Greg Arone

Description

Around 1982 Nick Kuhn proved that the symmetric powers of the sphere spectrum give rise to a minimal projective resolution of $HZ$. He then asked if there were other interesting examples of small projective resolutions of spectra, in particular of spectra like $bo$ or $bu$. In this talk I will show how to construct a small projective resolution of the connective K-theory spectrum $bu$. Our resolution has many similarities to the classic one that arises from the symmetric powers filtration. We give a unified proof of exactness of both resolutions, that is different from Kuhn’s proof. A key ingredient in our proof is a vanishing result for the Bredon homology of the complex of partitions and the complex of direct-sum decompositions. Joint work with Kathryn Lesh.

Auteur principal

Greg Arone (Stockholm)

Documents de présentation

Aucun document.
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