GENERATORS OF H 1 ( h ; Z) FOR TRIANGULATED SURFACES: Construction And Classification

We consider a bounded Lipschitz-polyhedron Ω R³ of general topology equipped with a tetrahedral triangulation that induces a mesh h of the surface @ We seek a maximal set of surface edge cycles that are independent in H1( h ; Z) and bounding with respect to the exterior of We present an algorithm for constructing suitable 1-cycles in h : First, representatives of a basis of the homology group H1( h ; Z) are constructed, merely using the combinatorial description of the surface mesh h . Then, a duality pairing based on linking numbers is used to determine those combinations that are bounding w.r.t. R n This is the key to circumventing a triangulation of the exterior region R in the computations. For shape-regular, quasiuniform families of meshes, the asymptotic complexity of the algorithm is shown to be O(N ), where N is the number of edges of h . The schem