Torsional Topological Invariants

TL;DR

This paper derives new topological invariants involving torsion using Lorentz algebra, including identities of Pontryagin and Euler types, some purely torsional, expanding the understanding of torsional topological properties.

Contribution

It introduces two series of Gauss-Bonnet type identities involving torsion, with some being purely torsional topological invariants, a novel extension in topological invariants.

Findings

Derived torsional Gauss-Bonnet type identities

Identified purely torsional topological invariants

Expanded the mathematical framework of torsion-related topological properties

Abstract

Making use of the SO(3,1) Lorentz algebra, we derive in this paper two series of Gauss-Bonnet type identities involving torsion, one being of the Pontryagin type and the other of the Euler type. Two of the six identities involve only torsional tensorial entities and are purely torsional topological invariants.