The G-index of a closed, spin, hyperbolic manifold of dimension 2 or 4

TL;DR

This paper introduces methods for calculating the G-index of closed, spin, hyperbolic manifolds in dimensions 2 and 4, and applies these to a specific hyperbolic 4-manifold with symmetric spin structure.

Contribution

The paper develops general techniques for computing the G-index of certain hyperbolic manifolds and applies them to a specific example, advancing understanding of geometric invariants.

Findings

Computed the G-index for the Davis hyperbolic 4-manifold.

Developed new techniques for G-index calculation in hyperbolic manifolds.

Extended methods to both 2- and 4-dimensional cases.

Abstract

In this paper, we develop general techniques for computing the G-index of a closed, spin, hyperbolic 2- or 4-manifold, and apply these techniques to compute the G-index of the fully symmetric spin structure of the Davis hyperbolic 4-manifold.