In mathematics, in the area of symplectic topology, relative contact homology is an invariant of spaces together with a chosen subspace.
It is a part of a more general invariant known as symplectic field theory, and is defined using pseudoholomorphic curves.
The simplest case yields invariants of Legendrian knots inside contact three-manifolds.
The relative SFT of this pair is a differential graded algebra; Ng derives a powerful knot invariant from a combinatorial version of the zero-th degree part of the homology.
It has the form of a finitely presented tensor algebra over a certain ring of multivariable Laurent polynomials with integer coefficients.