Outputs (33)

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.

Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance (2018)
Journal Article
Miller, A. N., & Powell, M. (2018). Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance. Algebraic & geometric topology, 18(6), 3425-3476. https://doi.org/10.2140/agt.2018.18.3425

We give a formula for the duality structure of the 3 –manifold obtained by doing zero-framed surgery along a knot in the 3 –sphere, starting from a diagram of the knot. We then use this to give a combinatorial algorithm for computing the twisted Blan... Read More about Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance.

Satellites and concordance of knots in 3-manifolds (2018)
Journal Article
Friedl, S., Nagel, M., Orson, P., & Powell, M. (2019). Satellites and concordance of knots in 3-manifolds. Transactions of the American Mathematical Society, 371(4), 2279-2306. https://doi.org/10.1090/tran/7313

Given a 3–manifold Y and a free homotopy class in [S1, Y ], we investigate the set of topological concordance classes of knots in Y × [0, 1] representing the given homotopy class. The concordance group of knots in the 3–sphere acts on this set. We sh... Read More about Satellites and concordance of knots in 3-manifolds.

Smooth and topological almost concordance (2018)
Journal Article
Nagel, M., Orson, P., Park, J., & Powell, M. (2019). Smooth and topological almost concordance. International Mathematics Research Notices, 2019(23), 7324-7355. https://doi.org/10.1093/imrn/rnx338

We investigate the disparity between smooth and topological almost concordance of knots in general 3-manifolds Y. Almost concordance is defined by considering knots in Y modulo concordance in Y × [0, 1] and the action of the concordance group of knot... Read More about Smooth and topological almost concordance.

Twisted Blanchfield pairings and decompositions of 3-manifolds (2017)
Journal Article
Friedl, S., Leidy, C., Nagel, M., & Powell, M. (2017). Twisted Blanchfield pairings and decompositions of 3-manifolds. Homology, Homotopy and Applications, 19(2), 275-287. https://doi.org/10.4310/hha.2017.v19.n2.a14

We prove a decomposition formula for twisted Blanchfield pairings of 3-manifolds. As an application we show that the twisted Blanchfield pairing of a 3-manifold obtained from a 3-manifold Y with a representation ϕ:Z[π1(Y)]→R, infected by a knot J alo... Read More about Twisted Blanchfield pairings and decompositions of 3-manifolds.

Stable classification of 4-manifolds with 3-manifold fundamental groups (2017)
Journal Article
Kasprowski, D., Land, M., Powell, M., & Teichner, P. (2017). Stable classification of 4-manifolds with 3-manifold fundamental groups. Journal of Topology, 10(3), 827-881. https://doi.org/10.1112/topo.12025

We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w2-type and their equivariant intersectio... Read More about Stable classification of 4-manifolds with 3-manifold fundamental groups.

Grope metrics on the knot concordance set (2017)
Journal Article
Cochran, T. D., Harvey, S., & Powell, M. (2017). Grope metrics on the knot concordance set. Journal of Topology, 10(3), 669-699. https://doi.org/10.1112/topo.12018

To a special type of grope embedded in 4-space, that we call a branchsymmetric grope, we associate a length function for each real number q ≥ 1. This gives rise to a family of pseudo-metrics d q , refining the slice genus metric, on the set of concor... Read More about Grope metrics on the knot concordance set.

Concordance Invariance of Levine-Tristram Signatures of Links (2017)
Journal Article
Nagel, M., & Powell, M. (2017). Concordance Invariance of Levine-Tristram Signatures of Links. Documenta Mathematica, 22, 25-43

We determine for which complex numbers on the unit circle the Levine-Tristram signature and the nullity give rise to link concordance invariants.