No Access Submitted: 17 December 2020 Accepted: 09 February 2021 Published Online: 10 March 2021
J. Math. Phys. 62, 032503 (2021); https://doi.org/10.1063/5.0040956
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• Samantha Allen
• Jacob H. Swenberg
Let X be a (2 + 1)-dimensional globally hyperbolic spacetime with a Cauchy surface Σ whose universal cover is homeomorphic to $R2$. We provide empirical evidence suggesting that the Jones polynomial detects causality in X. We introduce a new invariant of certain tangles related to the Conway polynomial and prove that the Conway polynomial does not detect the connected sum of two Hopf links among relevant three-component links, which suggests that the Conway polynomial does not detect causality in the scenario described.
The authors would like to thank Vladimir Chernov and Ina Petkova for their guidance throughout the project. The authors would also like to thank Gage Martin for helpful comments. S.A. would like to thank Charles Livingston for a helpful conversation. J.H.S. would like to thank Vanessa Pinney for her insight on enumeration of links. J.H.S. received support from NSF Grant No. DMS-1711100.
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