The Internet Archive has a preservation copy of this work in our general collections.
The file type is
The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of simplicial and cubical subdivisions of manifolds and, especially, spheres. We describe important constructions which allow to study all these combinatorial objects by means of methods of commutative and homological algebra. The proposed approach to combinatorialarXiv:math/0010073v1 fatcat:zs2jp5zs6vcedpym7nh7utk66e