Do Link Polynomials Detect Causality In Globally Hyperbolic Spacetimes?

Abstract

Let $X$ be a $(2+1)$-dimensional globally hyperbolic spacetime with a Cauchy surface $\Sigma$ whose universal cover is homeomorphic to ${\mathbb{R}}^2$. 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 3-component links, which suggests that the Conway polynomial does not detect causality in the scenario described.

18 pages, 14 figures

References in corpus (1)

• Khovanov homology and causality in spacetimes