Spectral asymmetry for manifolds of special holonomy

TL;DR

This paper introduces a spectral asymmetry measure for G_2 and Spin(7) manifolds, linking it to characteristic classes and special covariant forms, advancing understanding of their geometric invariants.

Contribution

It defines a new spectral asymmetry invariant for special holonomy manifolds and relates it to characteristic classes and defining forms.

Findings

Spectral asymmetry can be computed via characteristic classes.

The invariant is explicitly linked to covariant constant forms.

Provides a new tool for studying geometric properties of G_2 and Spin(7) manifolds.

Abstract

We define a measure of spectral asymmetry for G_2 and Spin(7) manifolds. We show that this invariant can be computed in terms of characteristic classes and the covariant constant form defining the G_2 or Spin(7) structure.