Главная

Mikiya Masuda

  1. Lattice multi-polygons.

    Втр, 04/03/2012 - 15:01 — SomNambul
    Authors: Mikiya Masuda, Akihiro Higashitani
    Subjects: Combinatorics
    Abstract

    We discuss generalizations of some results on lattice polygons to certain
    piecewise linear loops which may have a self-intersection but have vertices in
    the lattice $\Z^2$. We first prove a formula on the rotation number of a
    unimodular sequence in $\Z^2$ using toric topology. This formula implies the
    generalized twelve-point theorem.

  2. Classification of real Bott manifolds and acyclic digraphs.

    Пт, 06/25/2010 - 15:01 — SomNambul
    Authors: Mikiya Masuda, Sang-il Oum, Suyoung Choi
    Subjects: Algebraic Topology
    Abstract

    We completely characterize real Bott manifolds up to diffeomorphism in terms
    of three simple matrix operations on square binary matrices obtained from
    strictly upper triangular matrices by permuting rows and columns
    simultaneously. We also prove that any graded ring isomorphism between the
    cohomology rings of real Bott manifolds with $\Z/2$ coefficients is induced by
    an affine diffeomorphism between the real Bott manifolds.

  3. Classification of Q-trivial Bott manifolds.

    Чт, 12/31/2009 - 16:01 — SomNambul
    Authors: Mikiya Masuda, Suyoung Choi
    Subjects: Algebraic Topology
    Abstract

    A Bott manifold is a closed smooth manifold obtained as the total space of an
    iterated $\C P^1$-bundle starting with a point, where each $\C P^1$-bundle is
    the projectivization of a Whitney sum of two complex line bundles. A
    \emph{$\Q$-trivial Bott manifold} of dimension $2n$ is a Bott manifold whose
    cohomology ring is isomorphic to that of $(\CP^1)^n$ with $\Q$-coefficients. We
    find all diffeomorphism types of $\Q$-trivial Bott manifolds and show that they
    are distinguished by their cohomology rings with $\Z$-coefficients.

  4. Buchstaber invariants of skeleta of a simplex.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Yukiko Fukukawa, Mikiya Masuda
    Subjects: Algebraic Topology
    Abstract

    A moment-angle complex $\mathcal{Z}_K$ is a compact topological space
    associated with a finite simplicial complex $K$. It is realized as a subspace
    of a polydisk $(D^2)^m$, where $m$ is the number of vertices in $K$ and $D^2$
    is the unit disk of the complex numbers $\C$, and the natural action of a torus
    $(S^1)^m$ on $(D^2)^m$ leaves $\mathcal{Z}_K$ invariant. The Buchstaber
    invariant $s(K)$ of $K$ is the maximum integer for which there is a subtorus of
    rank $s(K)$ acting on $\mathcal{Z}_K$ freely.

Math-arch

RSS-материал