Outputs (33)

Embedded surfaces with infinite cyclic knot group (2023)
Journal Article
Conway, A., & Powell, M. (2023). Embedded surfaces with infinite cyclic knot group. Geometry & Topology, 27(2), 739-821. https://doi.org/10.2140/gt.2023.27.739

We study locally flat, compact, oriented surfaces in 4-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus g, to be related by an ambient homeomorphism, a... Read More about Embedded surfaces with infinite cyclic knot group.

Simply-connected manifolds with large homotopy stable classes (2022)
Journal Article
Conway, A., Crowley, D., Powell, M., & Sixt, J. (2023). Simply-connected manifolds with large homotopy stable classes. Journal of the Australian Mathematical Society, 115(2), 172-203. https://doi.org/10.1017/s1446788722000167

For every k ≥ 2 and n ≥ 2 we construct n pairwise homotopically inequivalent simply-connected, closed 4k-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic intersection form and is stab... Read More about Simply-connected manifolds with large homotopy stable classes.

The Z-Genus of Boundary Links (2022)
Journal Article
Feller, P., Park, J., & Powell, M. (2023). The Z-Genus of Boundary Links. Revista Matemática Complutense, 36(1), 1-25. https://doi.org/10.1007/s13163-022-00424-3

The Z-genus of a link L in S3 is the minimal genus of a locally at, embedded, connected surface in D4 whose boundary is L and with the fundamental group of the complement innite cyclic. We characterise the Z-genus of boundary links in terms of their... Read More about The Z-Genus of Boundary Links.

Four-manifolds up to connected sum with complex projective planes (2022)
Journal Article
Kaprowski, D., Powell, M., & Teichner, P. (2022). Four-manifolds up to connected sum with complex projective planes. American Journal of Mathematics, 144(1), 75-118. https://doi.org/10.1353/ajm.2022.0001

Based on results of Kreck, we show that closed, connected 4- manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the se... Read More about Four-manifolds up to connected sum with complex projective planes.

Embedding spheres in knot traces (2021)
Journal Article
Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M., & Ray, A. (2021). Embedding spheres in knot traces. Compositio Mathematica, 157(10), 2242-2279. https://doi.org/10.1112/s0010437x21007508

The trace of the n-framed surgery on a knot in S3 is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere whose compleme... Read More about Embedding spheres in knot traces.

Characterisation of homotopy ribbon discs (2021)
Journal Article
Conway, A., & Powell, M. (2021). Characterisation of homotopy ribbon discs. Advances in Mathematics, 391, Article 107960. https://doi.org/10.1016/j.aim.2021.107960

Let Γ be either the infinite cyclic group Z or the Baumslag-Solitar group Zn Z[ 1 2 ]. Let K be a slice knot admitting a slice disc D in the 4-ball whose exterior has fundamental group Γ. We classify the Γ-homotopy ribbon slice discs for K up to topo... Read More about Characterisation of homotopy ribbon discs.

Two-solvable and two-bipolar knots with large four-genera (2021)
Journal Article
Cha, J. C., Miller, A. N., & Powell, M. (2021). Two-solvable and two-bipolar knots with large four-genera. Mathematical Research Letters, 28(2), 331-382. https://doi.org/10.4310/mrl.2021.v28.n2.a2

For every integer g, we construct a 2-solvable and 2-bipolar knot whose topological 4-genus is greater than g. Note that 2-solvable knots are in particular algebraically slice and have vanishing Casson–Gordon obstructions. Similarly all known smooth... Read More about Two-solvable and two-bipolar knots with large four-genera.

Doubly slice knots and metabelian obstructions (2021)
Journal Article
Orson, P., & Powell, M. (2022). Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14(4), 847-873. https://doi.org/10.1142/s1793525321500229

An n-dimensional knot Sn⊂Sn+2 is called doubly slice if it occurs as the cross section of some unknotted (n+1)-dimensional knot. For every n it is unknown which knots are doubly slice, and this remains one of the biggest unsolved problems in high-dim... Read More about Doubly slice knots and metabelian obstructions.

Homotopy ribbon concordance and Alexander polynomials (2020)
Journal Article
Friedl, S., & Powell, M. (2020). Homotopy ribbon concordance and Alexander polynomials. Archiv der Mathematik, 115(6), 717-725. https://doi.org/10.1007/s00013-020-01517-5

We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L, then the Alexander polynomial of L divides the Alexander polynomial of J.

Triple linking numbers and surface systems (2020)
Journal Article
Davis, C. W., Nagel, M., Orson, P., & Powell, M. (2020). Triple linking numbers and surface systems. Indiana University Mathematics Journal, 69(7), 2505-2547. https://doi.org/10.1512/iumj.2020.69.8081

We give a refined value group for the collection of triple linking numbers of links in the 3–sphere. Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the li... Read More about Triple linking numbers and surface systems.