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Hiroaki Ishida

  1. Invariant stably complex structures on topological toric manifolds.

    Чт, 02/24/2011 - 16:01 — SomNambul
    Authors: Hiroaki Ishida
    Subjects: Differential Geometry
    Abstract

    We show that any $(\C ^*)^n$-invariant stably complex structure on a
    topological toric manifold of dimension $2n$ is integrable. We also show that
    such a manifold is weakly $(\C ^*)^n$-equivariantly isomorphic to a toric
    manifold.

  2. (Filtered) cohomological rigidity of Bott towers.

    Пнд, 06/28/2010 - 15:01 — SomNambul
    Authors: Hiroaki Ishida
    Subjects: Algebraic Topology
    Abstract

    A Bott tower is an iterated $\CP ^1$-bundle over a point, where each $\CP
    ^1$-bundle is the projectivization of a rank $2$ decomposable complex vector
    bundle. For a Bott tower, the filtered cohomology is naturally defined. We show
    that isomorphism classes of Bott towers are distinguished by their filtered
    cohomology rings. We even show that any filtered cohomology ring isomorphism
    between two Bott towers is induced by an isomorphism of the Bott towers.

  3. Symplectic real Bott manifolds.

    Пт, 01/22/2010 - 16:01 — SomNambul
    Authors: Hiroaki Ishida
    Subjects: Symplectic Geometry
    Abstract

    A real Bott manifold is the total space of an iterated $\RP ^1$-bundles over
    a point, where each $\RP^1$-bundle is the projectivization of a Whitney sum of
    two real line bundles. In this paper, we characterize real Bott manifolds which
    admit a symplectic form. In particular, it turns out that a real Bott manifold
    admits a symplectic form if and only if it is cohomologically symplectic. In
    this case, it admits even a K\"{a}hler structure. We also prove that any
    symplectic cohomology class of a real Bott manifolds can be represented by a
    symplectic form.

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