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Higher equivariant excision
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Dotto, Emanuele (2017) Higher equivariant excision. Advances in Mathematics, 309 . pp. 1-96. doi:10.1016/j.aim.2017.01.004 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2017.01.004
Abstract
We develop a theory of Goodwillie calculus for functors between G-equivariant homotopy theories, where G is a finite group. We construct J-excisive approximations for any finite G-set J. These combine into a poset, the Goodwillie tree, that extends the classical Goodwillie tower. We prove convergence results for the tree of a functor on pointed G-spaces that commutes with fixed-points, and we reinterpret the Tom Dieck-splitting as an instance of a more general splitting phenomenon that occurs for the fixed-points of the equivariant derivatives of these functors. As our main example we describe the layers of the tree of the identity functor in terms of the equivariant Spanier-Whitehead duals of the partition complexes.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Functor theory, Homotopy theory, G-spaces | ||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||
Publisher: | Academic Press | ||||||||
ISSN: | 0001-8708 | ||||||||
Official Date: | 17 March 2017 | ||||||||
Dates: |
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Volume: | 309 | ||||||||
Page Range: | pp. 1-96 | ||||||||
DOI: | 10.1016/j.aim.2017.01.004 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 12 September 2019 | ||||||||
Date of first compliant Open Access: | 19 September 2019 |
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