arXiv Open Access 2014

Knots and distributive homology: from arc colorings to Yang-Baxter homology

Jozef H. Przytycki

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Abstrak

This paper is a sequel to my essay "Distributivity versus associativity in the homology theory of algebraic structures" Demonstratio Math., 44(4), 2011, 821-867 (arXiv:1109.4850 [math.GT]). We start from naive invariants of arc colorings and survey associative and distributive magmas and their homology with relation to knot theory. We outline potential relations to Khovanov homology and categorification, via Yang-Baxter operators. We use here the fact that Yang-Baxter equation can be thought of as a generalization of self-distributivity. We show how to define and visualize Yang-Baxter homology, in particular giving a simple description of homology of biquandles.

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math.GT math.AT

Penulis (1)

Jozef H. Przytycki

Format Sitasi

APA MLA BibTeX

Przytycki, J.H. (2014). Knots and distributive homology: from arc colorings to Yang-Baxter homology. https://arxiv.org/abs/1409.7044

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Informasi Jurnal

Tahun Terbit: 2014
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓