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

Baader, Sebastian; Kjuchukova, Alexandra (2020). Symmetric quotients of knot groups and a filtration of the Gordian graph. Mathematical proceedings of the Cambridge Philosophical Society, 169(1), pp. 141-148. Cambridge University Press 10.1017/s0305004119000136

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We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The nth 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Baader, Sebastian

Subjects:

500 Science > 510 Mathematics

ISSN:

0305-0041

Publisher:

Cambridge University Press

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

27 Jan 2021 16:46

Last Modified:

14 Mar 2021 06:44

Publisher DOI:

10.1017/s0305004119000136

ArXiv ID:

1711.08144

Uncontrolled Keywords:

57M25

BORIS DOI:

10.48350/151219

URI:

https://boris.unibe.ch/id/eprint/151219

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