期刊
GEOMETRIAE DEDICATA
卷 147, 期 1, 页码 357-387出版社
SPRINGER
DOI: 10.1007/s10711-010-9458-y
关键词
Combinatorial topology; Finite topological space; Cell complex; Homology; Orientability; Poincare duality theorem
类别
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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