A Dirac Morphism for the Farrell-Jones Isomorphism Conjecture in K-Theory

TL;DR

This paper introduces a Dirac morphism approach to address the Farrell-Jones Isomorphism Conjecture in algebraic K-theory, linking the invertibility of this morphism to the conjecture's validity.

Contribution

It constructs a Dirac morphism and proves its invertibility implies the conjecture, providing a new method to approach the problem.

Findings

Dirac morphism constructed for the conjecture

Invertibility of the morphism implies the isomorphism conjecture

Provides a new framework for algebraic K-theory

Abstract

We construct a Dirac morphism and prove that if this Dirac morphism is invertible, then the isomorphism conjecture for non-connective algebraic K-theory holds true.