A Quick Note On Homsets and Diagrams

Sam Nelson

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arXiv · 2504.14384

A Quick Note On Homsets and Diagrams

Sam Nelson

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Abstract

The homset invariant of a knot or link L with respect to an algebraic knot coloring structure X can be identified with a set of colorings of a diagram of L by elements of X via an identification of diagrammatic generators with algebraic generators. In some cases, particularly when either L or X has a high degree of symmetry, distinct homset elements can be represented by superficially similar X-colored diagrams, potentially leading to confusion. In this short note we examine and attempt to clarify this phenomenon.

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Sam Nelson. 2025-04-19. A Quick Note On Homsets and Diagrams. https://arxiv.org/abs/2504.14384

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