Khovanov homology and causality in spacetimes

Abstract

We observe that Khovanov homology detects causality in (2 + 1)-dimensional globally hyperbolic spacetimes whose Cauchy surface is homeomorphic to R 2 .2010 Mathematics Subject Classification. 53C50 (Primary); 57M27, 83C75, 83C80 (Secondary).

Do Link Polynomials Detect Causality In Globally Hyperbolic Spacetimes?

“…The sky S x is homeomorphic to a circle, and viewed as a subset of the solid torus S 1 × R 2 , S x is isotopic to S 1 × {0}. For more explanation, see [CMP20] or [NT04].…”

“…Another common link polynomial is the Alexander-Conway polynomial (also called the Conway polynomial ) ∇(L), which is categorified by link Floer homology [KS16]. Chernov, Martin, and Petkova have suggested that link Floer homology will also detect causality in this setting [CMP20]. The related knot polynomials, the Jones polynomial and the Conway polynomial, are strictly weaker link invariants than their respective categorifications.…”

“…By a remark in [CMP20], if an invariant can detect causality in X as described, then causality can be detected in any (2 + 1)-dimensional globally hyperbolic spacetime X whose Cauchy surface Σ is not homeomorphic to S 2 or RP 2 . The reason is that the universal cover X of such a spacetime is also a globally hyperbolic spacetime with Cauchy surface Σ that is a universal cover of Σ .…”