Spin structures on 3–manifolds via arbitrary triangulations

Riccardo Benedetti, Petronio Carlo
2014 Algebraic and Geometric Topology  
Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra combinatorial structures on T. We then analyze how to change these extra structures on T, and T itself, without changing s, thereby getting a combinatorial realization, in the usual "objects/moves" sense, of the set of all pairs (M,s). Our moves have a local
more » ... es have a local nature, except one, that has a global flavour but is explicitly described anyway. We also provide an alternative approach where the global move is replaced by simultaneous local ones.
doi:10.2140/agt.2014.14.1005 fatcat:ezoraouuvvc5rbacxfw2bc4gmq