Surface cubications mod flips Louis Funar

Surface cubications mod flips Louis Funar Institut Fourier BP 74, UMR 5582 CNRS, University of Grenoble I, 38402 Saint-Martin-d'Heres cedex, France e-mail: September 20, 2007 Abstract Let ? be a compact surface. We prove that the set of marked surface cubications modulo flips, up to isotopy, is in one-to-one correspondence with Z/2Z ?H1(?, ∂?; Z/2Z). MSC Classification(2000): 05 C 10, 57 R 70, 55 N 22, 57 M 35. Keywords and phrases: cubication, surface, critical point, cobordism, immersion. 1 Introduction and statements Cubical complexes and marked cubications. A cubical complex is a finite dimensional complex C consisting of Euclidean cubes, such that the intersection of two of its cubes is a finite union of cubes from C, once a cube is in C then all its faces belong to C and each point has a neighborhood intersecting only finitely many cubes of C. A cubication of a topological manifold is a cubical complex that is homeomorphic to the manifold. If the manifold is a PL manifold then one requires that the cubication be combinatorial and compatible with the PL structure. Our definition of cubication is slightly more general than the usual one, because we don't require that the intersection of two cubes consists of a single cube but only a finite union of cubes.

• cubical complexes


• immersion


• higher dimensional


• there exist topological


• boundary


• dimensional manifold


• has


• manifold