Global orthogonal spectra

TL;DR

This paper introduces the concept of global orthogonal spectra, providing a unified framework for G-equivariant spectra across all finite groups using enriched indexed categories.

Contribution

It develops the definition of global orthogonal spectra and extends key theories like equivariant K-theory and Spin^c-cobordism to this global setting.

Findings

Defined global orthogonal spectra using enriched indexed categories

Extended Atiyah--Bott--Shapiro orientation to the global context

Unified treatment of G-equivariant spectra for all finite groups

Abstract

For any finite 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 finite group G. We use the framework of enriched indexed categories to make this precise. We also consider equivariant K-theory and Spin^c-cobordism from this perspective, and we show that the Atiyah--Bott--Shapiro orientation extends to the global context.