The v_n-periodic Goodwillie tower on Wedges and Cofibres

2016/12/08 by Brantner, Lukas, Heuts, Gijs
#55P42 #55P65 #55Q20 #55Q51 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.02694

Abstract

We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge X \vee Y of spaces (using the Hilton-Milnor theorem) and on the cofibre cof(f) of a map f: X → Y. We deduce some consequences for v_n-periodic homotopy groups: whereas the Goodwillie tower is finite and converges in periodic homotopy when evaluated on spheres (Arone-Mahowald), we show that neither of these statements remains true for wedges and Moore spaces.

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