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Note: Combinatorial Alexander Duality-A Short and Elementary Proof
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7497-2764
2009 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 42, no 4, 586-593 p.Article in journal (Refereed) Published
Abstract [en]

Let X be a simplicial complex with ground set V. Define its Alexander dual as the simplicial complex X* = {sigma subset of V vertical bar V \ sigma is not an element of X}. The combinatorial Alexander duality states that the ith reduced homology group of X is isomorphic to the (vertical bar V vertical bar - i - 3) th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof from first principles accessible to a nonexpert.

Place, publisher, year, edition, pages
2009. Vol. 42, no 4, 586-593 p.
Keyword [en]
Simplicial complex, Homology, Cohomology, Alexander dual, theorem
Identifiers
URN: urn:nbn:se:kth:diva-18900DOI: 10.1007/s00454-008-9102-xISI: 000271198900005Scopus ID: 2-s2.0-70449517513OAI: oai:DiVA.org:kth-18900DiVA: diva2:336947
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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Björner, Anders

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