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Yves Cornulier

  1. Bounded characteristic classes and flat bundles.

    Втр, 02/21/2012 - 15:01 — SomNambul
    Authors: Yves Cornulier, Indira Chatterji, Guido Mislin, Christophe Pittet
    Subjects: Algebraic Topology
    Abstract

    Let G be a connected Lie group, G^d the underlying discrete group, and BG,
    BG^d their classifying spaces. Let R denote the radical of G. We show that all
    classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R)
    are bounded if and only if the derived group [R,R] is simply connected. We also
    give equivalent conditions in terms of stable commutator length and distortion.

  2. On Property (FA) for wreath products.

    Пт, 04/16/2010 - 15:01 — SomNambul
    Authors: Yves Cornulier, Aditi Kar
    Subjects: Group Theory
    Abstract

    We characterize permutational wreath products with Property (FA). For
    instance, the standard wreath product A wr B of two nontrivial countable groups
    A,B, has Property (FA) if and only if B has Property (FA) and A is a finitely
    generated group with finite abelianisation. We also prove an analogous result
    for hereditary Property (FA). On the other hand, we prove that many wreath
    products with hereditary Property (FA) are not quotients of finitely presented
    groups with the same property.

  3. Embeddings of solvable Baumslag-Solitar groups into discrete groups with quadratic Dehn function.

    Втр, 03/02/2010 - 16:01 — SomNambul
    Authors: Yves Cornulier, Romain Tessera
    Subjects: Group Theory
    Abstract

    We embed the solvable Baumslag-Solitar groups in finitely presented
    metabelian groups with quadratic Dehn function.

  4. On the Cantor-Bendixson rank of metabelian groups.

    Чт, 01/07/2010 - 16:01 — SomNambul
    Authors: Yves Cornulier
    Subjects: Group Theory
    Abstract

    We study the Cantor-Bendixson rank of metabelian and virtually metabelian
    groups in the space of marked groups, and in particular, we exhibit a sequence
    (G_n) of 2-generated, finitely presented, virtually metabelian groups of
    Cantor-Bendixson rank omega^n.

  5. A characterization of relative Kazhdan Property T for semidirect products with abelian groups.

    Ср, 11/18/2009 - 16:01 — SomNambul
    Authors: Yves Cornulier, Romain Tessera
    Subjects: Group Theory
    Abstract

    Let A be a locally compact abelian group, and H a locally compact group
    acting on A. Let G=HA be the semidirect product. We prove that the pair (G,A)
    has Kazhdan's Property T if and only if the only H-invariant mean on the Borel
    subsets of the Pontryagin dual of A, supported at the neighbourhood of the
    trivial character, is the Dirac measure.

  6. Contracting automorphisms and L^p-cohomology in degree one.

    Ср, 08/19/2009 - 19:30 — SomNambul
    Authors: Yves Cornulier, Romain Tessera
    Subjects: Group Theory
    Abstract

    We characterize those Lie groups, and algebraic groups over a local field of
    characteristic zero, whose first reduced L^p-cohomology is zero for all p>1,
    extending a result of Pansu. As an application, we obtain a description of
    Gromov-hyperbolic groups among those groups. In particular we prove that any
    non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local
    field of zero characteristic is quasi-isometric to a 3-regular tree.

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