An $L_{\mathrm{\infty }}$ structure on symplectic cohomology

We construct the $L_{\mathrm{\infty }}$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed–open map to an $L_{\mathrm{\infty }}$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya category. Features of our construction are that it respects a modified action filtration (in contrast to Pomerleano–Seidel’s construction); it uses a compact telescope model (in contrast to Abouzaid–Groman–Varolgunes’ construction); and it is adapted to the purposes of our follow-up work where we construct Maurer–Cartan elements in symplectic cochains which are associated to a normal-crossings compactification of the Liouville domain.