2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104639This paper is a continuation of hepth/0507224 where open topological B-models describing D-branes on 2-cycles of local Calabi--Yau geometries with conical singularities were studied. After a short review, the paper expands in particular on two aspects: the gauge fixing problem in the reduction to two dimensions and the quantum matrix model solutions.17 p. To appear in proc. Symposium QTS-4, Varna (Bulgaria), August 2005High Energy Physics - Theorytext