Combinatorial spin structures on triangulated manifolds

TL;DR

This paper introduces a combinatorial approach to describe spin and spin^c-structures on triangulated PL-manifolds, facilitating computations by leveraging the naturality of binary symmetric groups to avoid complex smoothings.

Contribution

It provides a novel combinatorial framework for spin and spin^c-structures on triangulated manifolds, emphasizing computational efficiency and avoiding explicit smoothings.

Findings

Provides a combinatorial description of spin structures

Utilizes naturality of binary symmetric groups

Simplifies computations on triangulated manifolds

Abstract

This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary symmetric groups to avoid lengthy explicit constructions of smoothings of PL-manifolds.