A Fast, Strong, Topologically Meaningful and Fun Knot Invariant
3 days ago
- #Knot Theory
- #Polynomial Invariants
- #Geometric Topology
- Introduction of a pair of polynomial knot invariants Θ=(Δ,θ) with notable properties.
- Θ is theoretically and practically fast, computable in polynomial time on large knots (300+ crossings).
- Strong separation power surpassing hyperbolic volume, HOMFLY-PT polynomial, and Khovanov homology on knots up to 15 crossings.
- Topologically meaningful, likely providing a genus bound and potentially more insights.
- Δ is the Alexander polynomial, while θ is related to an invariant studied by Ohtsuki, Rozansky, Kricker, and Garoufalidis.
- Simplified formulas, proofs, and programs enable computation on very large knots.