Bordered LSFT algebras are defined for half-knots, and a pushout theorem recovers Ng's commutative LSFT algebra of the whole Legendrian knot.
Differential algebra of Legendrian links.Inventiones mathematicae, 150(3):441–483, 2002
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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.