Knot contact homology
WebAug 5, 2004 · 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 … WebKnot contact homology is the homology of a differential graded algebra associated to a knot, the knot DGA (A,∂). By the general invariance result for Legendrian contact …
Knot contact homology
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WebKnot contact homology, a topological link invariant of K, is defined as the Legendrian homology of ΛK, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization ℝ×U∗ℝ3 with Lagrangian boundary condition ℝ×ΛK. We perform an explicit and complete ... Webthe Legendrian contact homology DGA of the conormal lift of a knot K and also generalize the combinatorial description of knot contact homology to many-component links. Here the conormal lift of a link K is a union Λ K of Legendrian tori in the unit cotangent bundle S∗R3 of R3 with the contact structure given as the kernel of the canonical 1 ...
WebKnot contact homology, a topological link invariant of K, is defined as the Legendrian homology of Λ K, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization R×U∗R3with Lagrangian boundary condition R×Λ K. WebProposition 3.1. Let L be a Legendrian knot in the standard contact 3-sphere. If the characteristic algebra of L is nontrivial, then so is its contact homology. Proof. Suppose …
Weband knots; we call this the contact homology of the braid or knot. Although the homology of a DGA is generally hard to compute, there is a relatively simple form for the 0-dimensional part HC0 of the contact homology, and we can compute HC0 explicitly for a large number of knots. We concentrate on the invariant HC0 because it is difficult in ... WebOn the symplectic / contact geometry side, we can study the Legendrian contact homology of the conormal legendrian to a knot. This invariant is pretty di cult to get our hands on, …
WebSep 10, 2008 · Keywords: Heegaard Floer homology; Contact geometry; Legendrian knot 1. Introduction A contact structure, ξ, on a closed oriented three-manifold, Y , is an oriented two-dimensional sub-bundle of the tangent bundle, TY, which is completely non-integrable. This means there do not exist surfaces embedded in Y whose tangent planes lie in ξ in ...
WebApr 5, 2024 · The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional ... femme zenWebProposition 3.1. Let L be a Legendrian knot in the standard contact 3-sphere. If the characteristic algebra of L is nontrivial, then so is its contact homology. Proof. Suppose that the contact homology CH(L) = ker∂ im∂ of L is trivial. Then, since ∂(1) = 0, it must be the case that im∂ contains the unit element 1. femmezeWeb2014 (English) In: Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, E-ISSN 1095-0753, Vol. 18, no 4, p. 827-956 Article in journal (Other academic) Published Abstract [en] We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. femme zakiWebOct 17, 2012 · Knot contact homology is a Floer-theoretic knot invariant derived from counting holomorphic curves in the cotangent bundle of \ (\mathbb {R}^ {3}\) with Lagrangian boundary condition on the... howden dike yarmWebAug 20, 2011 · We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial.We provide a number of … howden hungary kftWebSep 7, 2011 · The knot contact homology detects several classes of knots [7], and an enhancement of the knot contact homology is a complete invariant of knots [6]. ... 2-knot … howden distributor in saudi arabiaWebfact that knot contact homology recovers enough of the knot group (the fundamental group of the knot complement) to detect the unknot [Ng08] and torus knots, among others [GL]. femme yannick alléno