Segal models for equivariant incomplete infinite loop spaces

2025/10/28 by Bantelmann, Tjark
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2510.24298

Abstract

We model equivariant infinite loop spaces indexed on incomplete universes via suitable equivariant analogs of Γ-spaces. The choice of universe dictates a transfer system which in turn dictates the Segal condition on equivariant Γ-spaces. Equivariant Γ-spaces themselves come in different but equivalent guises interpolating between categories Γ as defined by Segal and Γ_G as defined by Shimakawa. The main application is the construction of Segal K-theory of normed permutative categories.

Related

• Equivariant complete Segal spaces
• A symmetric monoidal and equivariant Segal infinite loop space machine
• A short treatise on Equivariant Gamma spaces
• Equivariant infinite loop space theory, the space level story
• Complete Segal spaces arising from simplicial categories