An open string analogue of Viterbo functoriality

Liouville domains are a special type of symplectic manifolds with boundary (they have an everywhere defined Liouville flow, pointing outwards along the boundary). Symplectic cohomology for Liouville domains was introduced by Cieliebak-Floer-Hofer-Wysocki and Viterbo. The latter constructed a restriction (or transfer) map associated to an embedding of one Liouville domain into another.