Knot contact homology
نویسندگان
چکیده
منابع مشابه
Knot Contact Homology
The conormal lift of a linkK in R is a Legendrian submanifold ΛK in the unit cotangent bundle U R of R with contact structure equal to the kernel of the Liouville form. Knot 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 sy...
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We extend knot contact homology to a theory over the ring Z[λ±1, μ±1], with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in S 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 in...
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This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
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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 computations of transverse homology that demonstrate its effectiv...
متن کاملKnot and Braid Invariants from Contact Homology
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology of certain Legendrian tori in fivedimensional contact manifolds. We present several computations and derive a relation between the knot invarian...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2013
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2013.17.975