R/Z-valued index theory via geometric K-homology

TL;DR

This paper develops a geometric model of K-homology with R/Z coefficients using Baum-Douglas cycles, linking it to the relative eta-invariant through index pairings, thus advancing the understanding of index theory with coefficients.

Contribution

It introduces a geometric realization of K-homology with R/Z coefficients via a model based on Baum-Douglas cycles, connecting it to eta-invariants.

Findings

Provides a geometric model of K-homology with R/Z coefficients.

Establishes a relationship between this model and the relative eta-invariant.

Enhances the framework of index pairings with coefficients.

Abstract

A model of K-homology with coefficients in a mapping cone using the framework of the geometric cycles of Baum and Douglas is developed. In particular, this leads to a geometric realization of K-homology with coefficients in R/Z. In turn, this group is related to the relative eta-invariant via index pairings.