Classification of spin structures on 4-dimensional almost-flat manifolds
Classification of spin structures on 4-dimensional almost-flat manifolds
Almost-flat manifolds were defined by Gromov as a natural generalisation of flat manifolds and as such share many of their properties. Similarly to flat manifolds, it turns out that the existence of a spin structure on an almost-flat manifold is determined by the canonical orthogonal representation of its fundamental group. Utilising this, we classify the spin structures on all four-dimensional almost-flat manifolds that are not flat. Out of 127 orientable families, there are exactly 15 that are non-spin, the rest are in fact parallelizable.
253-266
Lutowski, Rafal
32d7424b-80cf-4652-80d4-4a24b030c5ca
Petrosyan, Nansen
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Szczepański, Andrzej
1cc30fc9-d563-44cc-93c1-702da342e585
Lutowski, Rafal
32d7424b-80cf-4652-80d4-4a24b030c5ca
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Szczepański, Andrzej
1cc30fc9-d563-44cc-93c1-702da342e585
Lutowski, Rafal, Petrosyan, Nansen and Szczepański, Andrzej
(2018)
Classification of spin structures on 4-dimensional almost-flat manifolds.
Mathematika, 64 (1), .
(doi:10.1112/S0025579317000560).
Abstract
Almost-flat manifolds were defined by Gromov as a natural generalisation of flat manifolds and as such share many of their properties. Similarly to flat manifolds, it turns out that the existence of a spin structure on an almost-flat manifold is determined by the canonical orthogonal representation of its fundamental group. Utilising this, we classify the spin structures on all four-dimensional almost-flat manifolds that are not flat. Out of 127 orientable families, there are exactly 15 that are non-spin, the rest are in fact parallelizable.
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ab_dim4_spin_structures_final
- Accepted Manuscript
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Accepted/In Press date: 7 September 2017
e-pub ahead of print date: 14 February 2018
Identifiers
Local EPrints ID: 414282
URI: http://eprints.soton.ac.uk/id/eprint/414282
ISSN: 0025-5793
PURE UUID: dc4958a4-cd00-4488-b1cd-cb34ca7b9efa
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Date deposited: 22 Sep 2017 16:31
Last modified: 16 Mar 2024 04:17
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Author:
Rafal Lutowski
Author:
Andrzej Szczepański
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