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Spin structures on
$3$–manifolds via arbitrary triangulations
Riccardo Benedetti and Carlo Petronio |
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Algebraic & Geometric Topology 14 (2014) 1005–1054
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Abstract |
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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. |
Keywords
$3$–manifold, spin structure, triangulation, spine
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Mathematical Subject Classification 2010
Primary: 57R15
Secondary: 57N10, 57M20
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References |
Publication
Received: 16 April 2013
Revised: 9 September 2013
Accepted: 15 September 2013
Published: 21 March 2014
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Authors |
| Riccardo Benedetti | |
| Dipartimento di Matematica Università di Pisa Largo Bruno Pontecorvo 5 I-56127 Pisa Italy |
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| http://www.dm.unipi.it/~benedett/ | |
| Carlo Petronio | |
| Dipartimento di Matematica Università di Pisa Largo Bruno Pontecorvo 5 I-56127 Pisa Italy |
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| http://www.dm.unipi.it/pages/petronio/public\_html/ | |
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