Homology, Homotopy and Applications

Global orthogonal spectra

Anna Marie Bohmann

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation