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G&T Monographs |
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Knot and braid invariants from contact homology I
Lenhard Ng
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Geometry & Topology 9 (2005)
247–297
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Abstract
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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.
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Keywords
contact homology, knot invariant, braid
representation, differential graded algebra
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Mathematical Subject Classification
Primary: 57M27
Secondary: 20F36, 53D35
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Publication
Received: 16 July 2004
Accepted: 13 January 2005
Published: 26 January 2005
Proposed: Yasha Eliashberg
Seconded: Robion Kirby, Joan Birman
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