Combinatorial spin structures on triangulated manifolds

Abstract

We give a combinatorial description of spin and ${spin}^c$–structures on triangulated manifolds of arbitrary dimension. These encodings of spin and ${spin}^c$–structures are established primarily for the purpose of aiding in computations. The novelty of the approach is that we rely heavily on the naturality of binary symmetric groups to avoid lengthy explicit constructions of smoothings of PL manifolds.