Hyperplane arrangements and Milnor fibrations
نویسندگان
چکیده
منابع مشابه
Hyperplane Arrangements and Milnor Fibrations
— There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the h...
متن کاملOn Milnor Fibrations of Arrangements
We use covering space theory and homology with local coefficients to study the Milnor fiber of a homogeneous polynomial. These techniques are applied in the context of hyperplane arrangements, yielding an explicit algorithm for computing the Betti numbers of the Milnor fiber of an arbitrary real central arrangement in C3, as well as the dimensions of the eigenspaces of the algebraic monodromy. ...
متن کاملMorse theory, Milnor fibers and hyperplane arrangements
Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW complex in which the number of p-cells equals the p-th betti number.
متن کاملMultinets, Parallel Connections, and Milnor Fibrations of Arrangements
The characteristic varieties of a space are the jump loci for homology of rank 1 local systems. The way in which the geometry of these varieties may vary with the characteristic of the ground field is reflected in the homology of finite cyclic covers. We exploit this phenomenon to detect torsion in the homology of Milnor fibers of projective hypersurfaces. One tool we use is the interpretation ...
متن کاملMorse Theory, Milnor Fibers and Minimality of Hyperplane Arrangements
Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW-complex in which the number of p-cells equals the p-th betti number. Combining this result with recent work of Papadima and Suciu, one obtains a characterization of when ...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2014
ISSN: 0240-2963
DOI: 10.5802/afst.1412