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Cheol-Hyun Cho

  1. Chern-Weil Maslov index and its orbifold analogue.

    Mon, 02/06/2012 - 15:01 — SomNambul
    Authors: Cheol-Hyun Cho, Hyung-Seok Shin
    Subjects: Symplectic Geometry
    Abstract

    We give Chern-Weil definitions of the Maslov indices of bundle pairs over a
    Riemann surface \Sigma with boundary, which consists of symplectic vector
    bundle on \Sigma and a Lagrangian subbundle on \partial{\Sigma} as well as its
    generalization for transversely intersecting Lagrangian boundary conditions. We
    discuss their properties and relations to the known topological definitions. As
    a main application, we extend Maslov index to the case with orbifold interior
    singularites, via curvature integral, and find also an analogous topological
    definition in these cases.

  2. Potentials of homotopy cyclic $\AI$-algebras.

    Tue, 01/05/2010 - 16:01 — SomNambul
    Authors: Cheol-Hyun Cho, Sangwook Lee
    Subjects: Quantum Algebra
    Abstract

    For an $\AI$-algebra with a cyclic inner product, a potential recording the
    structure constants can be defined. We show how to define a potential for a
    homotopy cyclic $\AI$-algebra. Also we give a proof of the decomposition
    theorem for filtered $\AI$-algebras.

  3. On the obstructed Lagrangian Floer theory.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Cheol-Hyun Cho
    Subjects: Symplectic Geometry
    Abstract

    Lagrangian Floer homology in a general case has been constructed by Fukaya,
    Oh, Ohta and Ono, where they construct an $\AI$-algebra or an $\AI$-bimodule
    from Lagrangian submanifolds, and studied the obstructions and deformation
    theories. But for obstructed Lagrangian submanifolds, standard Lagrangian Floer
    homology can not be defined.

  4. On the obstructed Lagrangian Floer theory.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Cheol-Hyun Cho
    Subjects: Symplectic Geometry
    Abstract

    Lagrangian Floer homology in a general case has been constructed by Fukaya,
    Oh, Ohta and Ono, where they construct an $\AI$-algebra or an $\AI$-bimodule
    from Lagrangian submanifolds, and studied the obstructions and deformation
    theories. But for obstructed Lagrangian submanifolds, standard Lagrangian Floer
    homology can not be defined.

  5. Gradient-like vector fields on a complex analytic variety.

    Fri, 08/14/2009 - 21:09 — SomNambul
    Authors: Cheol-Hyun Cho, Giovanni Marelli
    Subjects: Geometric Topology
    Abstract

    Given any Morse function $f$ on a Whitney stratified complex analytic variety
    of complex dimension $n$, we prove the existence of a stratified gradient-like
    vector field for $f$ such that the unstable set of a critical point $p$ on a
    stratum $S$ of complex dimension $s$ has real dimension $m(p)+n-s$ as was
    conjectured by Goresky and MacPherson.

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