Torsion in one-term distributive homology

• Autorzy: Alissa S. Crans , Józef H. Przytycki , Krzysztof K. Putyra
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 18G60: Other (co)homology theories
• 55N35: Other homology theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 225
• Numer: 1
• Strony: 75-94

Daty

wydano

2014

Twórcy

autor

Alissa S. Crans

• Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045, U.S.A.

autor

Józef H. Przytycki

• Department of Mathematics, George Washington University, Washington, DC 20052, U.S.A.
• Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland

autor

Krzysztof K. Putyra

• Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.

Identyfikatory

DOI

10.4064/fm225-1-5