Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Global orthogonal spectra

Pages: 313 – 332

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n1.a17

Author

Anna Marie Bohmann (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Abstract

For any compact Lie group $G$, there are several well-established definitions of a $G$-equivariant spectrum. In this paper, we develop the definition of a global orthogonal spectrum. Loosely speaking, this is a coherent choice of orthogonal $G$-spectrum for each compact Lie group $G$. We use the framework of enriched indexed categories to make this precise. We also consider equivariant $K$-theory and $\operatorname{Spin}^c$-cobordism from this perspective, and we show that the Atiyah-Bott-Shapiro orientation extends to the global context.

Keywords

equivariant homotopy, homotopy, spectra, global

2010 Mathematics Subject Classification

55P42, 55P91

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