On some adjunctions in equivariant stable homotopy theory

Hu, Po; Kriz, Igor; Somberg, Petr

doi:10.2140/agt.2018.18.2419

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On some adjunctions in equivariant stable homotopy theory

Po Hu, Igor Kriz and Petr Somberg

Algebraic & Geometric Topology 18 (2018) 2419–2442

DOI: 10.2140/agt.2018.18.2419

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.

Keywords

equivariant cohomology, adjoint functor

Mathematical Subject Classification 2010

Primary: 55P91, 55P92, 55N91

Secondary: 18A40

References

Publication

Received: 9 July 2017

Revised: 18 January 2018

Accepted: 24 February 2018

Published: 26 April 2018

Authors

Po Hu
Department of Mathematics Wayne State University Detroit, MI United States

Igor Kriz
Department of Mathematics University of Michigan Ann Arbor, MI United States

Petr Somberg
Mathematical Institute of MFF UK Praha 8 Czech Republic

Volume 18, issue 4 (2018)