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Selman Akbulut

  1. Twisting 4-manifolds along RP^2.

    Чт, 12/24/2009 - 16:01 — SomNambul
    Authors: Selman Akbulut
    Subjects: Geometric Topology
    Abstract

    We prove that the Dolgachev surface E(1)_{2,3} (which is an exotic copy of
    the elliptic surface E(1)=CP^2 # 9(-CP^2)) can be obtained from E(1) by
    twisting along a simple "plug", in particular it can be obtained from E(1) by
    twisting along an RP^2.

  2. Cappell-Shaneson homotopy spheres are standard.

    Пт, 10/30/2009 - 16:01 — SomNambul
    Authors: Selman Akbulut
    Subjects: Geometric Topology
    Abstract

    We show that an infinite sequence of homotopy 4-spheres constructed by
    Cappell-Shaneson are all diffeomorphic to S^4. This generalizes previous
    results of Akbulut-Kirby and Gompf.

  3. Mirror Duality in a Joyce Manifold.

    Чт, 08/20/2009 - 23:06 — SomNambul
    Authors: Selman Akbulut, Baris Efe, Sema Salur
    Subjects: Geometric Topology
    Abstract

    Previously the two of the authors defined a notion of dual Calabi-Yau
    manifolds in a G_2 manifold, and described a process to obtain them. Here we
    apply this process to a compact G_2 manifold, constructed by Joyce, and as a
    result we obtain a pair of Borcea-Voisin Calabi-Yau manifolds, which are known
    to be mirror duals of each other.

  4. Small exotic Stein manifolds.

    Ср, 08/19/2009 - 19:30 — SomNambul
    Authors: Selman Akbulut, Kouichi Yasui
    Subjects: Geometric Topology
    Abstract

    It is known that the only Stein filling of the standard contact structure on
    S^3 is B^4. In this paper, we construct simply connected exotic compact Stein
    4-manifold pairs for any Betti number $b_2 \geq 1$; we do this by enlarging
    corks and plugs.

  5. Knotting corks.

    Ср, 08/19/2009 - 19:30 — SomNambul
    Authors: Selman Akbulut, Kouichi Yasui
    Subjects: Geometric Topology
    Abstract

    It is known that every exotic smooth structure on a simply connected closed
    4-manifold is determined by a codimention zero compact contractible Stein
    submanifold and an involution on its boundary. Such a pair is called a cork. In
    this paper, we construct infinitely many knotted imbeddings of corks in
    4-manifolds such that they induce infinitely many different exotic smooth
    structures.

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