133 research outputs found
Conormal bundles, contact homology and knot invariants
We summarize recent work on a combinatorial knot invariant called knot
contact homology. We also discuss the origins of this invariant in symplectic
topology, via holomorphic curves and a conormal bundle naturally associated to
the knot.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
A topological introduction to knot contact homology
This is a survey of knot contact homology, with an emphasis on topological,
algebraic, and combinatorial aspects.Comment: 38 pages, based on lectures at the Contact and Symplectic Topology
Summer School in Budapest, July 2012; v2: fixed typos, updated references,
version to be publishe
Combinatorial knot contact homology and transverse knots
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 effectiveness in distinguishing transverse knots, including
knots that cannot be distinguished by the Heegaard Floer transverse invariants
or other previous invariants.Comment: v2: 34 pages, minor corrections suggested by refere
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