Homology, Homotopy and Applications

Global orthogonal spectra

Anna Marie Bohmann

Full-text: Open access

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.

Article information

Source
Homology Homotopy Appl., Volume 16, Number 1 (2014), 313-332.

Dates
First available in Project Euclid: 3 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.hha/1401800085

Mathematical Reviews number (MathSciNet)
MR3217308

Zentralblatt MATH identifier
1356.55009

Subjects
Primary: 55P91: Equivariant homotopy theory [See also 19L47] 55P42: Stable homotopy theory, spectra

Keywords
Equivariant homotopy homotopy spectra global

Citation

Bohmann, Anna Marie. Global orthogonal spectra. Homology Homotopy Appl. 16 (2014), no. 1, 313--332. https://projecteuclid.org/euclid.hha/1401800085


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