Document Type
Article
Publication Date
8-2023
Abstract
We give diagrammatic algorithms for computing the group trisection, homology groups, and intersection form of a closed, orientable, smooth 4-manifold, presented as a branched cover of a bridge-trisected surface in 𝕊4. The algorithm takes as input a tri-plane diagram, labelled with permutations according to the Wirtinger relations. We apply our algorithm to several examples, including dihedral and cyclic covers of spun knots, cyclic covers of Suciu's ribbon knots with the trefoil knot group, and an infinite family of irregular covers of the Stevedore disk double. As an application, we give a fully automated algorithm for computing Kjuchukova's homotopy-ribbon obstruction for a p-colorable knot, given an extension of that coloring over a ribbon surface in the 4-ball.
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; Matic, Gordana; and Ruppik, Benjamin, "Algorithms for Computing Invariants of Trisected Branched Covers" (2023). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/202