A Note on Three-Fold Branched Covers of S⁴

Authors

Ryan Blair
Patricia Cahn, Smith CollegeFollow
Alexandra Kjuchukova, University of Wisconsin-Madison
Jeffrey Meier

Document Type

Article

Publication Date

2024

Publication Title

Ann. Inst. Fourier (Grenoble)

Abstract

We show that any 4-manifold admitting a (g;k₁,k₂,0)-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in S⁴, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property.

Volume

72

Issue

2

First Page

849

Last Page

866

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.

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Blair, Ryan; Cahn, Patricia; Kjuchukova, Alexandra; and Meier, Jeffrey, "A Note on Three-Fold Branched Covers of S⁴" (2024). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/180