Spin structures on 3–manifolds via arbitrary triangulations

Benedetti, Riccardo¹ ; Carlo, Petronio¹

¹Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

Algebraic and Geometric Topology, Tome 14 (2014) no. 2, pp. 1005-1054

Résumé

Let M be an oriented compact 3–manifold and let T be a (loose) triangulation of M with ideal vertices at the components 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 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.

Détail

DOI : 10.2140/agt.2014.14.1005

Classification : 57R15, 57N10, 57M20
Keywords: $3$–manifold, spin structure, triangulation, spine

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