Framed knot contact homology

By Lenhard L. Ng. 2004

94 citations recorded by the source corpus.

We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a two-variable polynomial knot invariant which is related to the $A$-polynomial.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/d6b61642feeaa6cc400aa176fa9ce4e8928dfeb1

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Citations in the corpus

A topological introduction to knot contact homology (2012, methodology): “Then we have (1) φB(A) = Φ L B ·A ·Φ R B ; see [Ng08, Ng11] for the proof.”
Legendrian Contact Homology in P X R (2005, methodology): “When n = 3, this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng [11, 12, 13].”
Legendrian contact homology in $P \times \mathbb{R}$ (2007, methodology): “This construction is the inspiration behind Ng’s exciting new invariants of knots in R3, [11, 12, 13].”
Non-triviality of the A-polynomial for knots in S^3 (2004, methodology): “de ST∗(R3). Lenny Ng has constructed a homology theory for knots in S3, the framed knot contact homology, which is strongly believed to be Eliashberg-Hofer of contact homology of the pair (ST∗(R3),L) [Ng]. Ng has shown that the A-polynomial can be derived from the simplest piece of the framed knot c”
Combinatorial knot contact homology and transverse knots (2010, methodology): “It was shown in [Ng08] that ÃK(λ, µ) contains the familiar A-polynomial of K as a factor.”
Knot contact homology (2011, methodology): “1, and consequently the framed knot DGA of [25], is a link invariant: two braids whose closures are isotopic links produce the same DGA up to equivalence (stable tame isomorphism).”