A graphical calculus for tangles in surfaces

Peter M. Johnson; Sóstenes Lins

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arXiv · 1210.6681

A graphical calculus for tangles in surfaces

Peter M. Johnson·Sóstenes Lins

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Abstract

We show how the theory of tangles is equivalent to that of well-connected tangles. These are drawn on a surface with boundary, and equivalent via Reidemeister moves of a restricted kind. This reworking of the graphical foundations for link and tangle theory can be expected to have a variety of applications, including ones involving 3-manifolds. It opens the way to new approaches for defining `facial' state-sum invariants that depend in part on assigning substates to faces of tangle diagrams.

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BibTeX RIS

Peter M. Johnson, Sóstenes Lins. 2013-02-15. A graphical calculus for tangles in surfaces. https://arxiv.org/abs/1210.6681

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