Matthias Nagel


Last Name

Nagel

First Name

Matthias

ORCID

0000-0002-5171-4420

Organisational unit

Filters

2021 - 20223
Reset filters

Search Results

Publications 1 - 3 of 3
  • Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
    Item type: Journal Article
    Friedl, Stefan; Kitayama, Takahiro; Lewark, Lukas; et al. (2022)
    Canadian Journal of Mathematics
    We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine-Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that for every knot K with nontrivial Alexander polynomial, there exists an infinite family of knots that are all concordant to K and have the same Blanchfield form as K, such that no pair of knots in that family is homotopy ribbon concordant.
  • Twisted signatures of fibered knots
    Item type: Journal Article
    Conway, Anthony; Nagel, Matthias (2021)
    Algebraic & Geometric Topology
    This paper concerns twisted signature invariants of knots and 3-manifolds. In the fibered case, we reduce the computation of these invariants to the study of the intersection form and monodromy on the twisted homology of the fiber surface. Along the way, we use rings of power series to obtain new interpretations of the twisted Milnor pairing introduced by Kirk and Livingston. This allows us to relate these pairings to twisted Blanchfield pairings. Finally, we study the resulting signature invariants, all of which are twisted generalizations of the Levine-Tristram signature.
  • Embedding spheres in knot traces
    Item type: Journal Article
    Feller, Peter; Miller, Allison N.; Nagel, Matthias; et al. (2021)
    Compositio Mathematica
    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 -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable -dimensional knot invariants. For each, this provides conditions that imply a knot is topologically n-shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice.
Publications 1 - 3 of 3