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Laurentiu Maxim

  1. L^2-Betti numbers of hypersurface complements.

    Tue, 02/07/2012 - 15:01 — SomNambul
    Authors: Laurentiu Maxim
    Subjects: Algebraic Topology
    Abstract

    In \cite{DJL07} it was shown that if $\scra$ is an affine hyperplane
    arrangement in $\C^n$, then at most one of the $L^2$--Betti numbers
    $b_i^{(2)}(\C^n\sm \scra,\id)$ is non--zero. In this note we prove an analogous
    statement for complements of complex affine hyperurfaces in general position at
    infinity. Furthermore, we recast and extend to this higher-dimensional setting
    results of \cite{FLM,LM06} about $L^2$--Betti numbers of plane curve
    complements.

  2. Hirzebruch classes of complex hypersurfaces.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann, Julius L. Shaneson
    Subjects: Algebraic Topology
    Abstract

    The Milnor-Hirzebruch class of a locally complete intersection X in an
    algebraic manifold M measures the difference between the (Poincare dual of the)
    Hirzebruch class of the virtual tangent bundle of X and, respectively, the
    Brasselet-Schuermann-Yokura (homology) Hirzebruch class of X. In this note, we
    calculate the Milnor-Hirzebruch class of a globally defined algebraic
    hypersurface X in terms of the corresponding Hirzebruch invariants of singular
    strata in a Whitney stratification of X.

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