Journal
GEOMETRIAE DEDICATA
Volume 147, Issue 1, Pages 357-387Publisher
SPRINGER
DOI: 10.1007/s10711-010-9458-y
Keywords
Combinatorial topology; Finite topological space; Cell complex; Homology; Orientability; Poincare duality theorem
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We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces, combinatorial cell complexes (or c.c.c). We define orientability, homology and cohomology of c.c.c's and develop enough algebraic topology in this setting to prove the Poincar, duality theorem for a c.c.c satisfying suitable regularity conditions. The definitions and proofs are completely finitary and combinatorial in nature.
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