Mathematical Research Letters

Volume 26 (2019)

Number 6

Universal surgery problems with trivial Lagrangian

Pages: 1587 – 1601



Michael Freedman (Microsoft Research Station Q, and Department of Mathematics, University of California at Santa Barbara)

Vyacheslav Krushkal (Department of Mathematics, University of Virginia, Charlottesville, Va., U.S.A.)


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