Geometry & Topology, Vol. 9 (2005) Paper no. 8, pages 247--297.

Knot and braid invariants from contact homology I

Lenhard Ng

Abstract. 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 five-dimensional contact manifolds. We present several computations and derive a relation between the knot invariant and the determinant.

Keywords. Contact homology, knot invariant, braid representation, differential graded algebra

AMS subject classification. Primary: 57M27. Secondary: 53D35, 20F36.

DOI: 10.2140/gt.2005.9.247

E-print: arXiv:math.GT/0302099

Submitted to GT on 16 July 2004. Paper accepted 13 January 2005. Paper published 26 January 2005.

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Lenhard Ng
Department of Mathematics, Stanford University
Stanford, CA 94305, USA

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