Change search
ReferencesLink to record
Permanent link

Direct link
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
URN: urn:nbn:se:kth:diva-18900DOI: 10.1007/s00454-008-9102-xISI: 000271198900005ScopusID: 2-s2.0-70449517513OAI: diva2:336947
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-12-14Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Björner, Anders
By organisation
Mathematics (Div.)
In the same journal
Discrete & Computational Geometry

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 25 hits
ReferencesLink to record
Permanent link

Direct link