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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

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.

equivariant cohomology, adjoint functor
Mathematical Subject Classification 2010
Primary: 55P91, 55P92, 55N91
Secondary: 18A40
Received: 9 July 2017
Revised: 18 January 2018
Accepted: 24 February 2018
Published: 26 April 2018
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