The degenerate distributive complex is degenerate

Jozef H. Przytycki; Krzysztof K. Putyra

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arXiv · 1411.5905

The degenerate distributive complex is degenerate

Jozef H. Przytycki·Krzysztof K. Putyra

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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 K\"unneth-type formula for the degenerate part. This solves the mystery in algebraic knot theory of the meaning of the degenerate quandle homology, brought over 15 years ago when the homology theories were defined, and the degenerate part was observed to be non trivial.

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Jozef H. Przytycki, Krzysztof K. Putyra. 2014-11-21. The degenerate distributive complex is degenerate. https://arxiv.org/abs/1411.5905

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