Knotting and linking in the Petersen family

2010/08/02 by Danielle O’Donnol, Danielle O'Donnol, O'Donnol, Danielle
Computer Science · Mathematics · #05C10 #57M15 #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:05C10 #msc:57M15 #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1008.0377

16 pages, 10 figures

arxiv created 2010/08/02 · openalex publication_date 2010/08/02 · arxiv updated 2010/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embedding and knotting in an embedding. We also present a more 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 particular cycles in the embedding.

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