Combinatorial spin structures on triangulated manifolds

Budney, Ryan

doi:10.2140/agt.2018.18.1259

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Combinatorial spin structures on triangulated manifolds

Ryan Budney

Algebraic & Geometric Topology 18 (2018) 1259–1279

DOI: 10.2140/agt.2018.18.1259

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.

Keywords

spin structures, triangulated manifolds, combinatorial spin structure

Mathematical Subject Classification 2010

Primary: 57R15

Secondary: 55S35, 57R05

References

Publication

Received: 11 October 2014

Revised: 30 October 2017

Accepted: 21 November 2017

Published: 3 April 2018

Authors

Ryan Budney
Mathematics and Statistics University of Victoria Victoria BC Canada

Volume 18, issue 3 (2018)