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Mathematics > Geometric Topology

arXiv:1804.07813 (math)
[Submitted on 20 Apr 2018]

Title:Topology change and selection rules for high-dimensional $\Spin(1, n)_0$-Lorentzian cobordisms

Authors:Gleb Smirnov, Rafael Torres
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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 $\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\Sl(2, \C)$-Lorentzian cobordisms between 3-manifolds and results of Reinhart and Sorkin on the existence of Lorentzian cobordisms. We compute the $\Spin(1, n)_0$-Lorentzian cobordism group for several dimensions. Restrictions on the gravitational kink numbers of $\Spin(1, n)_0$-weak Lorentzian cobordisms are obtained.
Subjects: Geometric Topology (math.GT); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Cite as: arXiv:1804.07813 [math.GT]
  (or arXiv:1804.07813v1 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1804.07813

Submission history

From: Rafael Torres [view email]
[v1] Fri, 20 Apr 2018 20:15:56 UTC (17 KB)
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