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arXiv:1306.4841 [math.GT]AbstractReferencesReviewsResources

Combinatorial spin structures on triangulated manifolds

Ryan Budney

Published 2013-06-20, updated 2014-10-11Version 2

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.

Comments: 17 pages, 4 figures: v2 has many edits to remove small errors. A more detailed exposition of the binary symmetric groups allows for a simpler motivation of the homotopy relation's definition involving an elementary shelling. Material not strictly needed for the primary results of the paper have been moved into the appendix
Categories: math.GT
Subjects: 57R15
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