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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 27, Issue 1


Goodwillie calculus and Whitehead products

Boris Chorny / Jérôme Scherer
Published Online: 2012-07-26 | DOI: https://doi.org/10.1515/forum-2012-0038


We prove that iterated Whitehead products of length (n + 1) vanish in any value of an n-excisive functor in the sense of Goodwillie. We compare then different notions of homotopy nilpotency, from the Berstein–Ganea definition to the Biedermann–Dwyer one. The latter is strongly related to Goodwillie calculus and we analyze the vanishing of iterated Whitehead products in such objects.

Keywords: Nilpotent; homotopy nilpotent; algebraic theory; Goodwillie calculus; excisive functor

MSC: 55Q15; 18C10; 55P47; 55P65; 55P3

About the article

Received: 2012-03-30

Revised: 2012-06-21

Published Online: 2012-07-26

Published in Print: 2015-01-01

Funding Source: FEDER/MEC

Award identifier / Grant number: MTM2010-20692

Citation Information: Forum Mathematicum, Volume 27, Issue 1, Pages 119–130, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0038.

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