String orientations of simplicial homology manifolds

TL;DR

This paper classifies string orientations of simplicial homology manifolds, which are a broad class of geometric objects relevant to space-time microstructure, using advanced algebraic topology tools.

Contribution

It introduces a classification of string orientations via cohomology and cobordism, extending the understanding of geometric structures beyond traditional manifolds.

Findings

String orientations are classified by H^3 with specific coefficients.

Cobordism classes of homology 3-spheres with trivial Rokhlin invariant are key.

Provides a framework linking topology and space-time microstructure.

Abstract

Simplicial homology manifolds are proposed as an interesting class of geometric objects, more general than topological manifolds but still quite tractable, in which questions about the microstructure of space-time can be naturally formulated. Their string orientations are classified by $H^3$ with coefficients in an extension of the usual group of D-brane charges, by cobordism classes of homology three-spheres with trivial Rokhlin invariant.