Lattices and manifolds of classes of flat tori Ramírez Uclés, Rafael Lattices Flat Rimannian Tori The topological and differentiable structures of some natural quotient spaces constructed from flat Riemannian tori are studied by means of a cut-and-paste procedure (concretely, Hn(Gl+(2;R)=Sl(2;Z)), where H = O+(2;R), CO+(2;R), O(2;R), CO(2;R)). In the orientation preserving cases, the quotients can be regarded as manifolds with singular points corresponding to lattices in the square and hexagonal crystal systems. In the non-orientation preserving ones, the natural structure is a smooth manifold with piecewise smooth boundary, where the interior points correspond to oblique lattices, the regular points of the boundary to rectangular and centered rectangular lattices and the edge of the boundary to square and hexagonal ones. 2020-12-03T09:04:50Z 2020-12-03T09:04:50Z 2010 journal article Ramírez, R. (2010) Lattices and manifolds of classes of flat tori Extracta Mathematicae, 25(2), 183-209 http://hdl.handle.net/10481/64641 spa open access