Spin structures on 3-manifolds via arbitrary triangulations

Abstract

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 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.

49 pages, many figures

References in corpus (1)

• Classical and quantum dilogarithmic invariants of flat PSL(2,C)-bundles over 3-manifolds

Cited by in corpus (3)

• Analytic families of quantum hyperbolic invariants
• The universal quantum invariant and colored ideal triangulations
• Combinatorial spin structures on triangulated manifolds