Osaka Journal of Mathematics

Knotting and linking in the Petersen family

Danielle O'Donnol

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Abstract

This paper extends the work of Nikkuni [4] finding an explicit relationship for the graph $K_{3, 3, 1}$ between knotting and linking, which relates the sum of the squares of linking numbers of links in the embedding and the second coefficient of the Conway polynomial of certain cycles in the embedding. Then we use this and other similar relationships to better understand the relationship between knotting and linking in the Petersen family. The Petersen family is the set of minor minimal intrinsically linked graphs. We prove that if such a spatial graph is complexly algebraically linked then it is knotted.

Article information

Source
Osaka J. Math., Volume 52, Number 4 (2015), 1079-1101.

Dates
First available in Project Euclid: 18 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1447856034

Mathematical Reviews number (MathSciNet)
MR3426630

Zentralblatt MATH identifier
1344.57004

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Citation

O'Donnol, Danielle. Knotting and linking in the Petersen family. Osaka J. Math. 52 (2015), no. 4, 1079--1101. https://projecteuclid.org/euclid.ojm/1447856034


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