Mathematical Research Letters
Volume 26 (2019)
Universal surgery problems with trivial Lagrangian
Pages: 1587 – 1601
We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for $4$‑dimensional surgery, is shown to admit Seifert surfaces with trivial Lagrangian. They are good boundary links [F82b], with Seifert matrices of a more general form than in known constructions of slice links. We show that a certain more restrictive condition on Seifert matrices is sufficient for proving the links are slice. We also give a correction of a Kirby calculus identity in [FK2], useful for constructing surgery kernels associated to linkslice problems.
Vyacheslav Krushkal was supported in part by NSF grant DMS-1612159.
Received 18 January 2019
Accepted 10 August 2019
Published 6 March 2020