Cosimplicial models for the limit of the Goodwillie tower

Eldred, Rosona

doi:10.2140/agt.2013.13.1161

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Cosimplicial models for the limit of the Goodwillie tower

Rosona Eldred

Algebraic & Geometric Topology 13 (2013) 1161–1182

DOI: 10.2140/agt.2013.13.1161

Abstract

We call attention to the intermediate constructions $T_{n} F$ in Goodwillie’s Calculus of homotopy functors, giving a new model which naturally gives rise to a family of towers filtering the Taylor tower of a functor. We also establish a surprising equivalence between the homotopy inverse limits of these towers and the homotopy inverse limits of certain cosimplicial resolutions. This equivalence gives a greatly simplified construction for the homotopy inverse limit of the Taylor tower of a functor $F$ under general assumptions.

Keywords

cosimplicial, Goodwillie Calculus, homotopy functor, homotopy limit, cofinal

Mathematical Subject Classification 2010

Primary: 55P65, 55P60

Secondary: 55P10

References

Publication

Received: 27 July 2011

Revised: 7 September 2012

Accepted: 7 September 2012

Published: 18 April 2013

Authors

Rosona Eldred
Department of Mathematics University of Hamburg Bundesstr. 55 D-20146 Hamburg Germany
http://www.math.uni-hamburg.de/home/eldred/

Volume 13, issue 2 (2013)