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11 Aug 2012
Homology of distributive lattices
 Józef H. Przytycki,
 Krzysztof K. Putyra
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We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semilattices, lattices and skew lattices. For every such a structure we define multiterm distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semilattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law.
Communicated by Jim Stasheff.
JHP was partially supported by the NSAAMS 091111 Grant, by the Polish Scientific Grant: Nr. NN201387034, and by the GWU REF Grant. KKP was supported by the NSF Grant DMS1005750 in summer 2011.
The paper is dedicated to Paweł Waszkiewicz (1973–2011), who was a faculty member of Theoretical Computer Science at Jagiellonian University in Krakow. He obtained PhD at the University of Birmingham, UK, in 2002 in the theory of domains and formal languages. Although his career has been ceased in a tragic manner 9 years later, he had already published 21 papers. The second author is indebted to him for being introduced to the fascinating world of categories, posets and domains.
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 Title
 Homology of distributive lattices
 Journal

Journal of Homotopy and Related Structures
Volume 8, Issue 1 , pp 3565
 Cover Date
 20130401
 DOI
 10.1007/s4006201200125
 Print ISSN
 21938407
 Online ISSN
 15122891
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Distributive homology
 Lattice
 Boolean algebra
 Spindle
 Multispindle
 Authors

 Józef H. Przytycki ^{(1)} ^{(2)}
 Krzysztof K. Putyra ^{(3)}
 Author Affiliations

 1. Department of Mathematics, George Washington University, Washington, DC, 20052, USA
 2. Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
 3. Department of Mathematics, Columbia University, New York, NY, 10027, USA