Journal: Mathematische Annalen

Abbreviation

Math. Ann.

Publisher

Springer

Journal Volumes

ISSN

1432-1807
0025-5831

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Publications 1 - 10 of 44
  • Almost positive links are strongly quasipositive
    Item type: Journal Article
    Feller, Peter; Lewark, Lukas; Lobb, Andrew (2023)
    Mathematische Annalen
    We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give a simple and complete characterization of link diagrams with quasipositive canonical surface (the surface produced by Seifert's algorithm). As applications, we determine which prime knots up to 13 crossings are strongly quasipositive, and we confirm the following conjecture for knots that have a canonical surface realizing their genus: a knot is strongly quasipositive if and only if the Bennequin inequality is an equality.
  • Zone diagrams in Euclidean spaces and in other normed spaces
    Item type: Journal Article
    Kawamura, Akitoshi; Matoušek, Jiří; Tokuyama, Takeshi (2012)
    Mathematische Annalen
  • The zeros of the Weierstrass ℘ –function and hypergeometric series
    Item type: Journal Article
    Duke, William; Imamoglu, Özlem (2008)
    Mathematische Annalen
  • Representations of integers as sums of an even number of squares
    Item type: Journal Article
    Imamoglu, Özlem; Kohnen, Winfried (2005)
    Mathematische Annalen
  • Integrality of volumes of representations
    Item type: Journal Article
    Bucher, Michelle; Burger, Marc; Iozzi, Alessandra (2021)
    Mathematische Annalen
    Let M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [3] we show that the volume of a representation ρ:π1(M)→Isom+(Hn), properly normalized, takes integer values if n is even and ≥4. If M is not compact and 3-dimensional, it is known that the volume is not locally constant. In this case we give explicit examples of representations with volume as arbitrary as the volume of hyperbolic manifolds obtained from M via Dehn fillings.
  • The Künneth formula in Floer homology for manifolds with restricted contact type boundary
    Item type: Journal Article
    Oancea, Alexandru (2006)
    Mathematische Annalen
  • Cannon-Thurstonmaps for CAT(0) groups with isolated flats
    Item type: Journal Article
    Beeker, Benjamin; Cordes, Matthew; Gardam, Giles; et al. (2022)
    Mathematische Annalen
    Mahan Mitra (Mj) proved Cannon–Thurston maps exist for normal hyperbolic subgroups of a hyperbolic group (Mitra in Topology, 37(3):527–538, 1998). We prove that Cannon–Thurston maps do not exist for infinite normal hyperbolic subgroups of non-hyperbolic $CAT(0)$ groups with isolated flats with respect to the visual boundaries. We also show Cannon–Thurston maps do not exist for infinite infinite-index normal $CAT(0)$ subgroups with isolated flats in non-hyperbolic $CAT(0)$ groups with isolated flats. We obtain a structure theorem for the normal subgroups in these settings and show that outer automorphism groups of hyperbolic groups have no purely atoroidal $ \mathbb{Z{^2}}$ subgroups.
  • Hofer geometry via toric degeneration
    Item type: Journal Article
    Kawamoto, Yusuke (2024)
    Mathematische Annalen
    The main theme of this paper is to use toric degeneration to study Hofer geometry by producing distinct homogeneous quasimorphisms on the group of Hamiltonian diffeomorphisms. We focus on the (complex n-dimensional) quadric hypersurface and the del Pezzo surfaces, and study two classes of distinguished Lagrangian submanifolds that appear naturally in a toric degeneration, namely the Lagrangian torus which is the monotone fiber of a Lagrangian torus fibration, and the Lagrangian spheres that appear as vanishing cycles. For the quadrics, we prove that the group of Hamiltonian diffeomorphisms admits two distinct homogeneous quasimorphisms and derive some superheaviness results. Along the way, we show that the toric degeneration is compatible with the Biran decomposition. This implies that for n = 2, the Lagrangian fiber torus (Gelfand–Zeitlin torus) is Hamiltonian isotopic to the Chekanov torus, which answers a question of Y. Kim. We prove analogous results for the del Pezzo surfaces. We also discuss applications to C⁰ symplectic topology.
  • Subconvex bounds on GL3 via degeneration to frequency zero
    Item type: Journal Article
    Holowinsky, Roman; Nelson, Paul D. (2018)
    Mathematische Annalen
Publications 1 - 10 of 44