E-theory Spectra for graded C*-algebras

TL;DR

This paper develops a new spectral framework for E-theory in graded C*-algebras, integrating algebraic topology with operator algebras to enhance understanding of their invariants.

Contribution

It introduces a generalization of orthogonal spectra to quasi-topological spaces for E-theory, including a graded product structure for separable C*-algebras.

Findings

Established a spectral model for E-theory in graded C*-algebras.

Enhanced the algebraic topology tools applicable to operator algebras.

Provided a framework for richer product structures in E-theory.

Abstract

This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first variable and a homology functor in the second variable but underlying goes from the category of separable C*-algebras and *-homomorphisms to the category of abelian groups and group homomorphisms. Here we create a generalisation of a orthogonal spectrum to quasi-topological spaces for E-theory. This includes a rich product structure in the context of graded separable C*-algebras.