Algebraic & Geometric Topology

Spin structures on $3$–manifolds via arbitrary triangulations

Riccardo Benedetti and Petronio Carlo

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 2 (2014), 1005-1054.

Received: 16 April 2013
Revised: 9 September 2013
Accepted: 15 September 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M20: Two-dimensional complexes

$3$–manifold spin structure triangulation spine


Benedetti, Riccardo; Carlo, Petronio. Spin structures on $3$–manifolds via arbitrary triangulations. Algebr. Geom. Topol. 14 (2014), no. 2, 1005--1054. doi:10.2140/agt.2014.14.1005.

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