Planar graphs deformations of bordered knot algebras

Peter Ozsvath; Zoltan Szabo

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arXiv · 2311.07503

Planar graphs deformations of bordered knot algebras

Peter Ozsvath·Zoltan Szabo

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Abstract

In an earlier paper, we introduced ``bordered knot algebras'', which are graded algebras indexed by a pair of integers (m,k). In a subsequent paper, we introduced a two-parameter family of differential graded algebra, the ``pong algebras'', and identified their homology with the bordered knot algebras, and characterized the induced A-infinity structure on the homology. The aim of the present paper is to give an explicit, combinatorial model for this A-infinity structure on the bordered knot algebras, and a further weighted deformation of this structure, in the case where k=1.

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Peter Ozsvath, Zoltan Szabo. 2023-11-13. Planar graphs deformations of bordered knot algebras. https://arxiv.org/abs/2311.07503

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