Bordered LSFT algebras are defined for half-knots, and a pushout theorem recovers Ng's commutative LSFT algebra of the whole Legendrian knot.
An L-infinity structure for Legendrian contact homology
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abstract
For any Legendrian knot or link in $\mathbb{R}^3$, we construct an $L_\infty$ algebra that can be viewed as an extension of the Chekanov-Eliashberg differential graded algebra. The $L_\infty$ structure incorporates information from rational Symplectic Field Theory and can be formulated combinatorially. One consequence is the construction of a Poisson bracket on commutative Legendrian contact homology, and we show that the resulting Poisson algebra is an invariant of Legendrian links under isotopy.
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Bordered Legendrian Rational Symplectic Field Theory
Bordered LSFT algebras are defined for half-knots, and a pushout theorem recovers Ng's commutative LSFT algebra of the whole Legendrian knot.