Algebraic & Geometric Topology

On some adjunctions in equivariant stable homotopy theory

Po Hu, Igor Kriz, and Petr Somberg

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Abstract

We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed points. This leads to a variety of interesting other adjunctions, including a chain of six (sometimes seven) adjoints involving the restriction functor to a subgroup of a finite group on equivariant spectra indexed over the trivial universe.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 4 (2018), 2419-2442.

Dates
Received: 9 July 2017
Revised: 18 January 2018
Accepted: 24 February 2018
First available in Project Euclid: 3 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1525312833

Digital Object Identifier
doi:10.2140/agt.2018.18.2419

Mathematical Reviews number (MathSciNet)
MR3797071

Zentralblatt MATH identifier
06867662

Subjects
Primary: 55P91: Equivariant homotopy theory [See also 19L47] 55P92: Relations between equivariant and nonequivariant homotopy theory 55N91: Equivariant homology and cohomology [See also 19L47]
Secondary: 18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)

Keywords
equivariant cohomology adjoint functor

Citation

Hu, Po; Kriz, Igor; Somberg, Petr. On some adjunctions in equivariant stable homotopy theory. Algebr. Geom. Topol. 18 (2018), no. 4, 2419--2442. doi:10.2140/agt.2018.18.2419. https://projecteuclid.org/euclid.agt/1525312833


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