Journal: Journal of Topology

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Publisher

Wiley

Journal Volumes

ISSN

1753-8424
1753-8416

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2015 - 201972020 - 20259
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Publications 1 - 10 of 16
  • Geometric invariant theory for graded unipotent groups and applications
    Item type: Journal Article
    Bérczi, Gergely; Doran, Brent; Hawes, Thomas; et al. (2018)
    Journal of Topology
  • Knotted families from graspers
    Item type: Journal Article
    Kosanović, Danica (2024)
    Journal of Topology
    For any smooth manifold M of dimension d ≥ 4, we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into M, in every degree that is a multiple of d - 3, and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the d-ball.
  • Double ramification cycles with target varieties
    Item type: Journal Article
    Janda, Felix; Pandharipande, Rahul; Pixton, Aaron; et al. (2020)
    Journal of Topology
    Let (Formula presented.) be a nonsingular projective algebraic variety over (Formula presented.), and let (Formula presented.) be the moduli space of stable maps (Formula presented.) from genus (Formula presented.), (Formula presented.) -pointed curves (Formula presented.) to (Formula presented.) of degree (Formula presented.). Let (Formula presented.) be a line bundle on (Formula presented.). Let (Formula presented.) be a vector of integers which satisfy (Formula presented.) Consider the following condition: the line bundle (Formula presented.) has a meromorphic section with zeros and poles exactly at the marked points (Formula presented.) with orders prescribed by the integers (Formula presented.). In other words, we require (Formula presented.) to be the trivial line bundle on (Formula presented.). A compactification of the space of maps based on the above condition is given by the moduli space of stable maps to rubber over (Formula presented.) and is denoted by (Formula presented.). The moduli space carries a virtual fundamental class (Formula presented.) in Gromov–Witten theory. The main result of the paper is an explicit formula (in tautological classes) for the push-forward via the forgetful morphism of (Formula presented.) to (Formula presented.). In case (Formula presented.) is a point, the result here specializes to Pixton's formula for the double ramification cycle proven in (Janda, Pandharipande, Pixton and Zvonkine, Publ. Math. Inst. Hautes Études Sci. 125 (2017) 221–266). Several applications of the new formula are given.
  • Structures in genus‐zero relative Gromov–Witten theory
    Item type: Journal Article
    Fan, Honglu; Wu, Longting; You, F. (2020)
    Journal of Topology
  • Gromov-Witten theory of complete intersections via nodal invariants
    Item type: Journal Article
    Argüz, Hülya; Bousseau, Pierrick; Pandharipande, Rahul; et al. (2023)
    Journal of Topology
    We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete intersections in projective space belong to the tautological ring of the moduli space of stable curves. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal Gromov-Witten invariants, we introduce the new notion of nodal relative Gromov-Witten invariants. We then prove a nodal degeneration formula and a relative splitting formula. These results for nodal relative Gromov-Witten theory are stated in complete generality and are of independent interest.
  • Commutative hairy graphs and representations of Out(F-r)
    Item type: Journal Article
    Willwacher, Thomas; Turchin, Victor (2017)
    Journal of Topology
  • Cubical accessibility and bounds on curves on surfaces
    Item type: Journal Article
    Beeker, Benjamin; Lazarovich, Nir (2017)
    Journal of Topology
  • Braids with as many full twists as strands realize the braid index
    Item type: Journal Article
    Feller, Peter; Hubbard, Diana (2019)
    Journal of Topology
  • Dual spaces of geodesic currents
    Item type: Journal Article
    De Rosa, Luca; Martínez-Granado, Dídac (2025)
    Journal of Topology
    Every geodesic current on a hyperbolic surface has an associated dual space. If the current is a lamination, this dual embeds isometrically into a real tree. We show that, in general, the dual space is a Gromov hyperbolic metric tree-graded space, and express its Gromov hyperbolicity constant in terms of the geodesic current. In the case of geodesic currents with no atoms and full support, such as those coming from certain higher rank representations, we show the duals are homeomorphic to the surface. We also analyze the completeness of the dual and the properties of the action of the fundamental group of the surface on the dual. Furthermore, we compare two natural topologies in the space of duals.
  • The simplicial volume of 3-manifolds with boundary
    Item type: Journal Article
    Bucher, Michelle; Frigerio, Roberto; Pagliantini, Cristina (2015)
    Journal of Topology
    We provide sharp lower bounds for the simplicial volume of compact -manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of 3-manifolds, including handlebodies and products of surfaces with the interval. Our results provide the first exact computation of the simplicial volume of a compact manifold whose boundary has positive simplicial volume. We also compute the minimal number of tetrahedra in a (loose) triangulation of the product of a surface with the interval.
Publications 1 - 10 of 16