The Z-Genus of Boundary Links

Feller, Peter; Park, Junghwan; Powell, Mark

Abstract

The Z-genus of a link L in S3 is the minimal genus of a locally at, embedded, connected surface in D4 whose boundary is L and with the fundamental group of the complement innite cyclic. We characterise the Z-genus of boundary links in terms of their single variable Blancheld forms, and we present some applications. In particular, we show that a variant of the shake genus of a knot, the Z-shake genus, equals the Z-genus of the knot.

Citation

Feller, P., Park, J., & Powell, M. (2023). The Z-Genus of Boundary Links. Revista Matemática Complutense, 36(1), 1-25. https://doi.org/10.1007/s13163-022-00424-3

• Journal Article Type: Article
• Acceptance Date: Mar 1, 2022
• Online Publication Date: Apr 15, 2022
• Publication Date: 2023-01
• Deposit Date: Mar 3, 2022
• Publicly Available Date: Mar 3, 2023
• Journal: Revista Matemática Complutense
• Print ISSN: 1139-1138
• Electronic ISSN: 1988-2807
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 1
• Pages: 1-25
• DOI: https://doi.org/10.1007/s13163-022-00424-3
• Public URL: https://durham-repository.worktribe.com/output/1213353
• Related Public URLs: https://arxiv.org/abs/2012.14367