Global orthogonal spectra

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.

17 pages

References in corpus (2)

• Global homotopy theory
• Enriched indexed categories

Cited by in corpus (8)

• Global homotopy theory
• Equivariant properties of symmetric products
• Symmetric spectra model global homotopy theory of finite groups
• Arnold Conjecture and Morava K-theory
• Global homotopy theory via partially lax limits
• Parametrized stability and the universal property of global spectra
• Realising ${\pi }_{\ast }^{e}R$-algebras by global ring spectra
• $G_{\infty }$-ring spectra and Moore spectra for $\beta$-rings