A splitting property of the chromatic homology of the complete graph

So Yamagata

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arXiv · 2301.01972

A splitting property of the chromatic homology of the complete graph

So Yamagata

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Abstract

Khovanov introduced a bigraded cohomology theory of links whose graded Euler characteristic is the Jones polynomial. The theory was subsequently applied to the chromatic polynomial of graph, resulting in a categorification known as the ``chromatic homology''. Much as in the Khovanov homology, the chromatic polynomial can be obtained by taking the Euler characteristic of the chromatic homology. In the present paper, we introduce a combinatorial description of enhanced states that can be applied to analysis of the homology in an explicit way by hand. Using the new combinatorial description, we show a splitting property of the chromatic homology for a certain class of graphs. Finally, as an application of the description, we compute the chromatic homology of the complete graph.

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So Yamagata. 2023-01-05. A splitting property of the chromatic homology of the complete graph. https://arxiv.org/abs/2301.01972

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