Global Homotopy Theory
By S. Schwede. 2018
166 citations recorded by the source corpus.
This book introduces a new context for global homotopy theory, i.e., equivariant homotopy theory with universal symmetries. Many important equivariant theories naturally exist not just for a particular group, but in a uniform way for all groups in a specific class. Prominent examples are equivariant stable homotopy, equivariant $K$-theory or equivariant bordism. Global equivariant homotopy theory studies such uniform phenomena, i.e., the adjective `global' refers to simultaneous and compatible actions of all compact Lie groups. We give a self-contained treatment of unstable and stable global homotopy theory, modeled by orthogonal spaces respectively orthogonal spectra under global equivalences. Specific topics include the global stable homotopy category, operations on equivariant homotopy groups, global model structures, and ultra-commutative multiplications. The book includes many explicit examples and detailed calculations.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4072cfc2effc65267c82a4ad2ecbd271cffbef89
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Citations in the corpus
- Nilpotence and descent in equivariant stable homotopy theory (2015, background): “These E∞-structures are established in work of Joachim [41], and appear in Schwede’s theory of global spectra [66].”
- LECTURES ON EQUIVARIANT STABLE HOMOTOPY THEORY (2016, background): “For a detailed exposition of orthogonal G-spectra in the generality of compact Lie groups, the reader may want to consult Chapter 3 of the author’s book [21].”