P-34 Classifying Links Obtained by Strong Fusion
Abstract
Band fusion modifies a link by fusing together two link components with a band, and its effect on links has been tabulated. We extend this work with an original analysis of the effects of strong fusion, a modified form of fusion that preserves the number of components of a link by introducing an unknotted component around the fusion band. In particular, we determine the exact effect of strong fusion on several link invariants, including the Q polynomial. We then use link invariants to classify which links are the result of strong fusion, tabulating all such links with up to 9 crossings.
Start Date
2-28-2020 2:30 PM
P-34 Classifying Links Obtained by Strong Fusion
Band fusion modifies a link by fusing together two link components with a band, and its effect on links has been tabulated. We extend this work with an original analysis of the effects of strong fusion, a modified form of fusion that preserves the number of components of a link by introducing an unknotted component around the fusion band. In particular, we determine the exact effect of strong fusion on several link invariants, including the Q polynomial. We then use link invariants to classify which links are the result of strong fusion, tabulating all such links with up to 9 crossings.
Acknowledgments
Mentor: Anthony Bosman, Mathematics
Undergraduate Research Scholars: Benjamin Dronen & Gabriel Palacios
J.N. Andrews Honors Scholar: Jonathan Homan