Dihedral Linking Invariants

Authors

Patricia Cahn, Smith CollegeFollow
Elise Catania, University of Minnesota
Sarangoo Chimgee, Smith College
Olivia Del Guercio, Rice University
Jack Kendrick, University of Washington

Document Type

Article

Publication Date

12-2021

Abstract

A Fox p-colored knot K in S³ gives rise to a p-fold branched cover M of S³ along K. The pre-image of the knot K under the covering map is a p+1/2-component link L in M, and the set of pairwise linking numbers of the components of L is an invariant of K. This powerful invariant played a key role in the development of early knot tables, and appears in formulas for many other important knot and manifold invariants. We give an algorithm for computing this invariant for all odd p, generalizing an algorithm of Perko, and tabulate the invariant for thousands of p-colorable knots.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

Licensed to Smith College and distributed CC-BY 4.0 under the Smith College Faculty Open Access Policy.

Version

Author's Submitted Manuscript

Recommended Citation

Cahn, Patricia; Catania, Elise; Chimgee, Sarangoo; Del Guercio, Olivia; and Kendrick, Jack, "Dihedral Linking Invariants" (2021). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/203