We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $ mathrm {Spin}(1, n)_0$. This extends a result of Gibbons-Hawking on $ mathrm {Sl}(2,mathbb{C})$-Lorentzian cobordisms between 3-manifolds and results of Reinhart and Sorkin on the existence of Lorentzian cobordisms. We compute the $ mathrm {Spin}(1, n)_0$-Lorentzian cobordism group for several dimensions. Restrictions on the gravitational kink numbers of $ mathrm {Spin}(1, n)_0$-weak Lorentzian cobordisms are obtained.

Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms / Smirnov, Gleb; Torres, Rafael. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 373:3(2020), pp. 1731-1747. [10.1090/tran/7939]

Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms

Smirnov, Gleb;Torres, Rafael
2020

Abstract

We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $ mathrm {Spin}(1, n)_0$. This extends a result of Gibbons-Hawking on $ mathrm {Sl}(2,mathbb{C})$-Lorentzian cobordisms between 3-manifolds and results of Reinhart and Sorkin on the existence of Lorentzian cobordisms. We compute the $ mathrm {Spin}(1, n)_0$-Lorentzian cobordism group for several dimensions. Restrictions on the gravitational kink numbers of $ mathrm {Spin}(1, n)_0$-weak Lorentzian cobordisms are obtained.
373
3
1731
1747
https://doi.org/10.1090/tran/7939
https://www.ams.org/journals/tran/2020-373-03/S0002-9947-2019-07939-4/
https://arxiv.org/abs/1804.07813
Smirnov, Gleb; Torres, Rafael
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/108858
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