The Z-genus of boundary links

Feller, P., Park, J. and Powell, M. (2023) The Z-genus of boundary links. Revista Matemática Complutense, 36(1), pp. 1-25. (doi: 10.1007/s13163-022-00424-3)

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Abstract

The Z-genus of a link L in S3 is the minimal genus of a locally flat, embedded, connected surface in D4 whose boundary is L and with the fundamental group of the complement infinite cyclic. We characterise the Z-genus of boundary links in terms of their single variable Blanchfield 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.

Item Type:Articles
Additional Information:PF gratefully acknowledges support by the SNSF Grant 181199. MP was partially supported by EPSRC New Investigator grant EP/T028335/1 and EPSRC New Horizons grant EP/V04821X/1.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Feller, P., Park, J., and Powell, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Revista Matemática Complutense
Publisher:Springer
ISSN:1139-1138
ISSN (Online):988-2807
Published Online:15 April 2022
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Revista Matemática Complutense 36(1): 1-25
Publisher Policy:Reproduced under a Creative Commons License

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