Detecting Causality with Symplectic Quandles

Ayush Jain

doi:10.1007/s11005-024-01808-w

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arXiv · 2310.06853

Detecting Causality with Symplectic Quandles

Ayush Jain

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Abstract

We investigate the capability of Symplectic quandles to detect causality for (2+1)-dimensional globally hyperbolic spacetimes (X). Allen and Swenberg showed that Alexander-Conway polynomial is insufficient to distinguish connected sum of two Hopf links from the links in the family of Allen-Swenberg 2-sky like links, suggesting that it can not always detect causality in X. We find that symplectic quandles, combined with Alexander-Conway polynomial, can distinguish these two type of links, thereby suggesting their ability to detect causality in X. The fact that symplectic quandles can capture causality in the Allen-Swenberg example is intriguing since the theorem of Chernov and Nemirovski, which states that Legendrian linking equals causality, is proved using Contact Geometry methods.

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Ayush Jain. 2023-09-17. Detecting Causality with Symplectic Quandles. https://doi.org/10.1007/s11005-024-01808-w

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