Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 2 (2014), 1005-1054.
Spin structures on $3$–manifolds via arbitrary triangulations
Let be an oriented compact –manifold and let be a (loose) triangulation of with ideal vertices at the components of and possibly internal vertices. We show that any spin structure on can be encoded by extra combinatorial structures on . We then analyze how to change these extra structures on , and itself, without changing , thereby getting a combinatorial realization, in the usual “objects/moves” sense, of the set of all pairs . 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.
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
Permanent link to this document
Digital Object Identifier
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
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