Lattices and manifolds of classes of flat tori Ramírez Uclés, Rafael Sánchez, Miguel The topological and differentiable structures of some moduli spaces constructed from flat Riemannian tori (concretely, H\(Gl(2,R)+/Sl(2, Z)), H = O+(2,R), CO+(2,R), O(2,R), CO(2,R)) is studied by means of a cut-and-paste procedure. In the orientation preserving cases, the quotients admit a structure of orbifold with singular points corresponding to lattices in the square and hexagonal crystal systems. In the non-orientation preserving ones, the structure is a smooth manifold with piecewise smooth boundary, where the interior points corresponds to oblique lattices, and the edge of the boundary to square and hexagonal ones. 2020-12-04T10:08:55Z 2020-12-04T10:08:55Z 2006-08 conference output Ramírez, R y Sánchez, M. (2006, agosto) Lattices and manifolds of classes of flat tori Póster presentado en el Internacional Congress of Mathematicians (ICM 2006). Publicado en el libro de actas, p. 51. Madrid, España. http://hdl.handle.net/10481/64668 eng open access