We investigate Landau-Ginzburg string theory with the singular superpo
tential X(-1) on arbitrary Riemann surfaces. This theory, which is a t
opological version of the c = 1 string at the self-dual radius, is sol
ved using results from intersection theory and from the analysis of ma
tter Landau-Ginzburg systems, and consistency requirements. Higher-gen
us amplitudes decompose as a sum of contributions from the bulk and th
e boundary of moduli space. These amplitudes generate the W-infinity a
lgebra.