New algorithms for computing bases of homology groups of two-dimensional pseudomanifolds

Background. The objects of research are two-dimensional compact polyhedra with an Euclidean cell decomposition, which are pseudomanifolds with boundary. The goal is to create new effective algorithms for computing the bases of absolute and relative homology groups modulo 2. Materials and methods. Proposed a reduction procedure to a similar problem for polyhedra of lesser dimensionality, containing fewer number of cells. Results. We develope algorithms which do not use incidence matrices. Their mathematical justification is given. Conclusions. For the class of polyhedra under consideration, the algorithms presented in this paper are much more efficient than the standard ones.