Journal of Symplectic Geometry

Volume 13 (2015)

Number 1

Transverse string topology and the cord algebra

Pages: 1 – 16

DOI: https://dx.doi.org/10.4310/JSG.2015.v13.n1.a1

Authors

Somnath Basu (Department of Mathematical Sciences, Binghamton University, Binghamton, New York, U.S.A.)

Jason McGibbon (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.)

Dennis Sullivan (Mathematics Department, Stony Brook University, Stony Brook, New York, U.S.A.)

Michael Sullivan (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

Abstract

We define a coalgebra structure for open strings transverse to any framed codimension $2$ submanifold $K \subset M$. When the submanifold is a knot in $\mathbb{R}^3$; we show this structure recovers a specialization of Ng cord algebra, a non-trivial knot invariant which is not determined by a number of other knot invariants.

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Published 8 April 2015