Spectral multiplicity and odd K-theory

TL;DR

This paper explores the space of unbounded self-adjoint Fredholm operators as a classifying space for odd K-theory, emphasizing the significance of eigenvalue multiplicities in understanding eigenspaces.

Contribution

It introduces a new perspective on odd K-theory by analyzing eigenvalue multiplicities within the space of unbounded self-adjoint Fredholm operators.

Findings

Eigenvalue multiplicity impacts the structure of the classifying space.

The study links eigenspace data to K^{1}(X) classification.

Framework for incorporating eigenspace information into K-theory.

Abstract

In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular, the role that the multiplicity of eigenvalues plays is developed here.