Document Type
Article - post-print
Publication Date
2013
Abstract
The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homology was initially suspected to be torsion-free, but we show in this paper that the one-term homology of a finite spindle can 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.
Original Publication Citation
Crans, A.; Przytycki, J.; and Putyra, K. “Torsion in one-term distributive homology.” Fundamenta Mathematicae. Vol. 225 (2014): 75 – 94.
Digital Commons @ LMU & LLS Citation
Crans, Alissa S.; Przytycki, Józef H.; and Putyra, Krzysztof K., "Torsion in one-term distributive homology" (2013). Mathematics, Statistics and Data Science Faculty Works. 67.
https://digitalcommons.lmu.edu/math_fac/67
Comments
This article is the post-print version.