Homotopy-theoretic E-theory and n-order

TL;DR

This paper demonstrates that various bootstrap categories in E-theory and G-equivariant E-theory have infinite n-order, highlighting their rich homotopical structure through a homotopy-theoretic approach.

Contribution

It establishes that the bootstrap categories in E-theory and G-equivariant E-theory possess infinite n-order by embedding them into homotopy categories of diagrams of K-module spectra.

Findings

Bootstrap categories in E-theory have infinite n-order.

Homotopy-theoretic embedding reveals the structure of these categories.

Results apply to G-equivariant E-theory and connective E-theory.

Abstract

The bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap category in G-equivariant E-theory for a compact group G and for the Spanier--Whitehead category in connective E-theory.