Geometriae Dedicata

, Volume 147, Issue 1, pp 357–387 | Cite as

Combinatorial cell complexes and Poincaré duality

Original Paper


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 Poincaré duality theorem for a c.c.c satisfying suitable regularity conditions. The definitions and proofs are completely finitary and combinatorial in nature.


Combinatorial topology Finite topological space Cell complex Homology Orientability Poincaré duality theorem 

Mathematics Subject Classification (2000)

05E25 06A07 06A11 55U05 55N35 55U10 55U15 57P10 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.IPMUUniversity of TokyoKashiwaJapan

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