# Goodwillie calculus and Whitehead products

@article{Scherer2015GoodwillieCA, title={Goodwillie calculus and Whitehead products}, author={J'erome Scherer and Boris Chorny}, journal={Forum Mathematicum}, year={2015}, volume={27}, pages={119-130} }

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.

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#### References

SHOWING 1-10 OF 26 REFERENCES

The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres

- Mathematics
- 1999

Abstract. We investigate Goodwillie's “Taylor tower” of the identity functor from spaces to spaces. More specifically, we reformulate Johnson's description of the Goodwillie derivatives of the… Expand

Homotopy nilpotent groups

- Mathematics
- 2007

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent… Expand

Nilpotence and finite H-spaces

- Mathematics
- 1989

Zabrodsky asked when is the iterated commutator mapXn →X for a connected associative H-spaceX a null map. In this paper we reduce this question to a cohomological question and answer it in several… Expand

Homotopical nilpotence of

- Mathematics
- 1964

In [1] Berstein and Ganea define the nilpotence of an H-space to be the least integer n such that the n-commutator is nullhomotopic. We prove that S3 with the usual multiplication is 4 nilpotent. Let… Expand

Simplicial Homotopy Theory

- Mathematics, Computer Science
- Modern Birkhäuser Classics
- 2009

Simplicial sets, model categories, and cosimplicial spaces: applications for homotopy coherence, results and constructions, and more. Expand

HOMOTOPICAL NILPOTENCE OF S3

- 2010

In [l] Berstein and Ganea define the nilpotence of an ü-space to be the least integer » such that the »-commutator is nullhomotopic. We prove that S3 with the usual multiplication is 4 nilpotent. Let… Expand

On products in homotopy groups

- Mathematics
- 1946

One of the outstanding problems in homotopy theory is that of determining the homotopy groups of simple spaces. Even for as simple a space as the n-sphere very little is known. In fact, in most… Expand

On the Homotopy Groups of the Union of Spheres

- Mathematics
- 1955

Let 8( be a sphere of dimension r,+ l, rt^ 1, i = 1, ..., h, and let T be the union of the spheres Sv ..., Sk, with a single common point. Then T serves as a universal example for homotopy… Expand

Algebraic theories in homotopy theory

- Mathematics
- 2001

It is well known in homotopy theory that given a loop space X one can always find a simplicial group G weakly equivalent to X, such that the weak equivalence can be realized by maps preserving… Expand

Stable homotopy of algebraic theories

- Mathematics
- 2001

Abstract The simplicial objects in an algebraic category admit an abstract homotopy theory via a Quillen model category structure. We show that the associated stable homotopy theory is completely… Expand