Knot and braid invariants from contact homology

Lenny Ng
Stanford University

We develop new topological invariants of knots and braids,
which take the form of differential graded algebras, and present an
explicit combinatorial formulation for these invariants. The algebras
give the relative contact homology of certain Legendrian tori in
five-dimensional contact manifolds. We will also relate our knot
invariant to the classical Alexander polynomial.

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