Cosimplicial models for the limit of the Goodwillie tower

Details Cosimplicial models for the limit of the Goodwillie tower Cosimplicial models for the limit of the Goodwillie tower

2011-07-30

arxiv.org/abs/1108.0114v2

Mathematics

Algebraic Topology

16 pages, changed title, changed statement of theorem giving model for the iterated T_n^k's, addressed Referee suggestions

Scientific paper

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 new 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.

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