Symmetric quotients of knot groups and a filtration of the Gordian graph

Sebastian Baader; Alexandra Kjuchukova

doi:10.1017/s0305004119000136

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arXiv · 1711.08144

Symmetric quotients of knot groups and a filtration of the Gordian graph

Sebastian Baader·Alexandra Kjuchukova

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Abstract

We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where all meridians are mapped to transpositions. Incidentally, we verify the Meridional Rank Conjecture for a family of knots with unknotting number one yet arbitrarily high bridge number.

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Sebastian Baader, Alexandra Kjuchukova. 2017-11-22. Symmetric quotients of knot groups and a filtration of the Gordian graph. https://doi.org/10.1017/s0305004119000136

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