Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 5 (2016), 857-875.

New examples of Brunnian theta graphs

Byoungwook Jang, Anna Kronaeur, Pratap Luitel, Daniel Medici, Scott Taylor, and Alexander Zupan

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Abstract

The Kinoshita graph is the most famous example of a Brunnian theta graph, a nontrivial spatial theta graph with the property that removing any edge yields an unknot. We produce a new family of diagrams of spatial theta graphs with the property that removing any edge results in the unknot. The family is parameterized by a certain subgroup of the pure braid group on four strands. We prove that infinitely many of these diagrams give rise to distinct Brunnian theta graphs.

Article information

Source
Involve, Volume 9, Number 5 (2016), 857-875.

Dates
Received: 17 August 2015
Revised: 20 October 2015
Accepted: 22 October 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371075

Digital Object Identifier
doi:10.2140/involve.2016.9.857

Mathematical Reviews number (MathSciNet)
MR3541985

Zentralblatt MATH identifier
1346.57010

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
spatial graph almost unknotted graph Brunnian theta graph theta curve rational tangle

Citation

Jang, Byoungwook; Kronaeur, Anna; Luitel, Pratap; Medici, Daniel; Taylor, Scott; Zupan, Alexander. New examples of Brunnian theta graphs. Involve 9 (2016), no. 5, 857--875. doi:10.2140/involve.2016.9.857. https://projecteuclid.org/euclid.involve/1511371075


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