Torsion in one-term distributive homology

Alissa S. Crans, Józef H. Przytycki, and Krzysztof K. Putyra. "Torsion in one-term distributive homology." Fundamenta Mathematicae 225.0 (2014): 75-94. <http://eudml.org/doc/286253>.

@article{AlissaS2014,
abstract = {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.},
author = {Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra},
journal = {Fundamenta Mathematicae},
keywords = {acyclicity; distributive homology; quandle; shelf; spindle},
language = {eng},
number = {0},
pages = {75-94},
title = {Torsion in one-term distributive homology},
url = {http://eudml.org/doc/286253},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Alissa S. Crans
AU - Józef H. Przytycki
AU - Krzysztof K. Putyra
TI - Torsion in one-term distributive homology
JO - Fundamenta Mathematicae
PY - 2014
VL - 225
IS - 0
SP - 75
EP - 94
AB - 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.
LA - eng
KW - acyclicity; distributive homology; quandle; shelf; spindle
UR - http://eudml.org/doc/286253
ER -