All Outputs (6)

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.

Splitting Numbers of Links (2017)
Journal Article
Cha, J. C., Friedl, S., & Powell, M. (2017). Splitting Numbers of Links. Proceedings of the Edinburgh Mathematical Society, 60(03), 587-614. https://doi.org/10.1017/s0013091516000420

The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and A... Read More about Splitting Numbers of Links.

A Calculation of Blanchfield Pairings of 3-Manifolds and Knots (2017)
Journal Article
Friedl, S., & Powell, M. (2017). A Calculation of Blanchfield Pairings of 3-Manifolds and Knots. Moscow mathematical journal, 17(1), 59-77

We calculate Blanchfield pairings of 3-manifolds. In particular, we give a formula for the Blanchfield pairing of a fibred 3-manifold and we give a new proof that the Blanchfield pairing of a knot can be expressed in terms of a Seifert matrix.