The algebra of rack and quandle cohomology

Clauwens, F. J. B. J.

doi:10.48550/arxiv.1004.4423

Cited by 2 publications

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“…with initial values r 0 = r 1 = 1. There is a similar exponential growth for homology of dihedral quandles [NP-2] which was explained by existence of homological operations [Cla,. This suggested there should be a similar story for homology of a distributive lattice.…”

Section: Computation Of Multi-term Homologymentioning

confidence: 76%

“…sets with a right self-distributive invertible binary operation) was introduced about 1990 by Fenn, Rourke and Sanderson [Fe, FRS] in relation to higher dimensional knot theory. The first full calculation of rack homology was that of prime dihedral quandles Nos,Cla]. In this paper we outline the general theory of multishelves and distributive homology.…”

Section: Introductionmentioning

confidence: 99%

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Homology of distributive lattices

Przytycki

Putyra

2012

J. Homotopy Relat. Struct.

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We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term 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 semi-lattices 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.

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Section: Computation Of Multi-term Homologymentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Homology of distributive lattices

Przytycki

Putyra

2012

J. Homotopy Relat. Struct.

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“…The Clauwens monoid and the rack space. Each augmented rack X π − → G embeds into a topological monoid that we call the Clauwens monoid of X π − → G (see [4]). One way to describe this construction is as follows [12].…”

Section: Introductionmentioning

confidence: 99%

“…Theorem Q 4. gives an isomorphism in homology, rather than homotopy, but this is sufficient since a connected monoid is homotopy simple.…”

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confidence: 99%