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Jie Wu

  1. The Functor $A^{\min}$ for $(p-1)$-cell Complexes and $\EHP$ Sequences.

    Fri, 02/05/2010 - 16:01 — SomNambul
    Authors: Jie Wu
    Subjects: Algebraic Topology
    Abstract

    Let $X$ be a co-$H$-space of $(p-1)$-cell complex with all cells in even
    dimensions. Then the loop space $\Omega X$ admits a retract $\bar A^{\min}(X)$
    that is the evaluation of the functor $\bar A^{\min}$ on $X$. In this paper, we
    determine the homology $H_*(\bar A^{\min}(X))$ and give the $\EHP$ sequence for
    the spaces $\bar A^{\min}(X)$.

  2. Symmetric ideals in group rings and simplicial homotopy.

    Tue, 02/02/2010 - 16:01 — SomNambul
    Authors: Roman Mikhailov, Jie Wu, Inder Bir S. Passi
    Subjects: Group Theory
    Abstract

    In this paper homotopical methods for the description of subgroups determined
    by ideals in group rings are introduced. It is shown that in certain cases the
    subgroups determined by symmetric product of ideals in group rings can be
    described with the help of homotopy groups of spheres.

  3. On modular signs.

    Fri, 11/13/2009 - 16:01 — SomNambul
    Authors: Jie Wu, Emmanuel Kowalski, Yuk Kam Lau
    Subjects: Number Theory
    Abstract

    We consider some questions related to the signs of Hecke eigenvalues or
    Fourier coefficients of classical modular forms. One problem is to determine to
    what extent those signs, for suitable sets of primes, determine uniquely the
    modular form, and we give both individual and statistical results. The second
    problem, which has been considered by a number of authors, is to determine the
    size, in terms of the conductor and weight, of the first sign-change of Hecke
    eigenvalues. Here we improve the recent estimate of Iwaniec, Kohnen and
    Sengupta.

  4. On Brunnian-type links and the link invariants given by homotopy groups of spheres.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Jie Wu
    Subjects: Algebraic Topology
    Abstract

    We introduce the (general) homotopy groups of spheres as link invariants for
    Brunnian-type links through the investigations on the intersection subgroup of
    the normal closures of the meridians of strongly nonsplittable links. The
    homotopy groups measure the difference between the intersection subgroup and
    symmetric commutator subgroup of the normal closures of the meridians and give
    the invariants of the links obtained in this way. Moreover the higher
    homotopy-group invariants can produce some links that could not be detected by
    the Milnor invariants.

  5. On homotopy groups of the suspended classifying spaces.

    Wed, 08/26/2009 - 14:58 — SomNambul
    Authors: Roman Mikhailov, Jie Wu
    Subjects: Algebraic Topology
    Abstract

    In this paper, we determine the homotopy groups $\pi_4(\Sigma K(G,1))$,
    $\pi_5(\Sigma K(G,1))$ and $\pi_5(\Sigma^2K(G,1))$ for different groups $G$ by
    using different facts and methods from group theory and homotopy theory:
    derived functors, the Carlsson simplicial construction, the Baues-Goerss
    spectral sequence, homotopy decompositions and the methods of algebraic
    K-theory.

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