Outputs (3)

Stabilization distance between surfaces (2019)
Journal Article
Miller, A. N., & Powell, M. (2019). Stabilization distance between surfaces. L’Enseignement mathématique, 65(3/4), 397-440. https://doi.org/10.4171/lem/65-3/4-4

Define the 1-handle stabilization distance between two surfaces properly embedded in a fixed 4-dimensional manifold to be the minimal number of 1-handle stabilizations necessary for the surfaces to become ambiently isotopic. For every nonnegative int... Read More about Stabilization distance between surfaces.

A family of freely slice good boundary links (2019)
Journal Article
Cha, J. C., Kim, M. H., & Powell, M. (2020). A family of freely slice good boundary links. Mathematische Annalen, 376(3-4), 1009-1030. https://doi.org/10.1007/s00208-019-01907-3

We show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two... Read More about A family of freely slice good boundary links.

Whitney towers and abelian invariants of knots (2019)
Journal Article
Cha, J. C., Orr, K., & Powell, M. (2020). Whitney towers and abelian invariants of knots. Mathematische Zeitschrift, 294(1-2), 519-553. https://doi.org/10.1007/s00209-019-02293-x

We relate certain abelian invariants of a knot, namely the Alexander polynomial, the Blanchfield form, and the Arf invariant, to intersection data of a Whitney tower in the 4-ball bounded by the knot. We also give a new 3-dimensional algorithm for co... Read More about Whitney towers and abelian invariants of knots.