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Goodwillie calculus and Whitehead products
-
Boris Chorny
and
Jérôme Scherer
Published/Copyright:
July 26, 2012
Abstract
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.
Funding source: FEDER/MEC
Award Identifier / Grant number: MTM2010-20692
We would like to thank Amnon Neeman and the Mathematical Sciences Institute at ANU where this project started. The hospitality of EPFL is greatly acknowledged by the first author, who visited the second author in order to complete this work. We learned about homotopy nilpotent groups from Georg Biedermann and Bill Dwyer and thank them for their interest in this project.
Received: 2012-3-30
Revised: 2012-6-21
Published Online: 2012-7-26
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Keywords for this article
Nilpotent;
homotopy nilpotent;
algebraic theory;
Goodwillie calculus;
excisive functor
Articles in the same Issue
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
