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arXiv · 1403.3419

Virtual knot theory on a group

Arnaud Mortier
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Abstract

Given a group endowed with a Z/2-valued morphism we associate a Gauss diagram theory, and show that for a particular choice of the group these diagrams encode faithfully virtual knots on a given arbitrary surface. This theory contains all of the earlier attempts to decorate Gauss diagrams, in a way that is made precise via symmetry-preserving maps. These maps become crucial when one makes use of decorated Gauss diagrams to describe finite-type invariants. In particular they allow us to generalize Grishanov-Vassiliev's formulas and to show that they define invariants of virtual knots.

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Arnaud Mortier. 2014-03-13. Virtual knot theory on a group. https://arxiv.org/abs/1403.3419

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