The degenerate distributive complex is degenerate

Józef Henryk Przytycki , Krzysztof K. Putyra

Abstract

We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology.In particular,when the multispindle is a quandle Q, the degenerate homology of Q is completely determined by the quandle homology of Q. For this case (and generally for two-term homology of a spindle) we provide an explicit Künneth-type formula for the degenerate part. This solves the mystery in algebraic knot theory of the meaning of the regenerate quandle homology, brought over 15 years ago when the homology theories were defined, and the degenerate part was observed to be nontrivial.
Author Józef Henryk Przytycki IM
Józef Henryk Przytycki,,
- Institute of Mathematics
, Krzysztof K. Putyra
Krzysztof K. Putyra,,
-
Journal seriesEuropean Journal of Mathematics, ISSN 2199-675X, e-ISSN 2199-6768
Issue year2016
Vol2
No4
Pages993-1012
Publication size in sheets1.2
Keywords in Englishspindle, quandle, rack homology, quandle homology, degenerate homology
DOIDOI:10.1007/s40879-016-0116-2
URL http://link.springer.com/content/pdf/10.1007%2Fs40879-016-0116-2.pdf
Languageen angielski
Score (nominal)5
ScoreMinisterial score = 0.0, 17-01-2018, ArticleFromJournal
Ministerial score (2013-2016) = 5.0, 17-01-2018, ArticleFromJournal - czasopismo zagraniczne spoza list
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