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Torsion in one-term distributive homology

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Crans A., Przytycki J., Putyra K.

Fundamenta Mathematicae

2014

tom 225

nr 1

75-94

The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely. In addition, we show that any finite group can appear as the torsion subgroup of the first homology of some finite spindle. Finally, we show that if a shelf satisfies a certain, rather general, condition then the one-term homology is trivial-this answers a conjecture from [Prz] affirmatively.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Crans A.

1 Przytycki J.

1 Putyra K.

1 2014

Wyniki wyszukiwania

Torsion in one-term distributive homology