Litcius/Paper detail

Models of G–spectra as presheaves ofspectra

Bertrand Guillou, J. P. May

2024Algebraic & Geometric Topology43 citationsDOIOpen Access PDF

Abstract

Let G be a finite group.We give Quillen equivalent models for the category of G-spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra.Our preferred model is based on equivariant infinite loop space theory applied to elementary categorical data.It recasts equivariant stable homotopy theory in terms of point-set-level categories of G-spans and nonequivariant spectra.We also give a more topologically grounded model based on equivariant Atiyah duality.55P42, 55P91, 55P92; 55P48 1.The bicategory GE and S -category GA 1228 2. The proof of the main theorem 1242 3. Some comparisons of functors 1254 4. Atiyah duality for finite G-sets 1258 Appendix A. Enriched model categories of G-spectra 1264 Appendix B. Whiskering GE to obtain strict unit 1-cells 1271

Topics & Concepts

Equivariant mapMathematicsFunctorCategorical variableSpectral linePure mathematicsHomotopyDuality (order theory)Space (punctuation)Algebra over a fieldPhysicsComputer scienceStatisticsQuantum mechanicsOperating systemHomotopy and Cohomology in Algebraic TopologyAlgebraic structures and combinatorial modelsAdvanced Topics in Algebra