## Algebraic & Geometric Topology

### 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 $∂M$ 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

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

Dates
Revised: 9 September 2013
Accepted: 15 September 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715856

Digital Object Identifier
doi:10.2140/agt.2014.14.1005

Mathematical Reviews number (MathSciNet)
MR3180826

Zentralblatt MATH identifier
1302.57061

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715856

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