Homotopy of planar Lie group equivariant presheaves

Scott Balchin

doi:10.1007/s40062-017-0193-z

Homotopy of planar Lie group equivariant presheaves

Scott Balchin

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Abstract

We utilise the theory of crossed simplicial groups to introduce a collection of local Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site. As an application, we give a characterisation of equivariant cohomology theories on a site as derived mapping spaces in these model categories.

Original language	English
Pages (from-to)	555–580
Number of pages	26
Journal	Journal of Homotopy and Related Structures
Volume	13
Early online date	02 Nov 2017
DOIs	https://doi.org/10.1007/s40062-017-0193-z
Publication status	Published - Sept 2018
Externally published	Yes

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10.1007/s40062-017-0193-zLicence: CC BY

Homotopy of planar Lie group equivariant presheaves
© 2024 The Authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 581 KBLicence: CC BY

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AB - We utilise the theory of crossed simplicial groups to introduce a collection of local Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site. As an application, we give a characterisation of equivariant cohomology theories on a site as derived mapping spaces in these model categories.

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Homotopy of planar Lie group equivariant presheaves

Abstract

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