Cohomology of Finite and Affine Type Artin Groups Over Abelian Representation

1. Auflage 2009
ISBN: 978-88-7642-345-1
Verlag: Scuola Normale Superiore

Buch, Englisch, 170 Seiten, Format (B × H): 154 mm x 245 mm, Gewicht: 364 g

Reihe: Theses (Scuola Normale Superiore)

The classical theory of braids is deeply connected with the theory of reflection groups and there are many relations between Artin groups and Coxeter groups. It turns out that the classifying spaces of Artin groups of finite type are affine varieties, the complement of the singularities associated to Coxeter groups.In order to study the topology of the Milnor fiber of these non-isolated singularities together with the monodromy action it is useful to compute the cohomology of the Artin groups with coefficients in an abelian representation.In this book a description of this cohomology for Artin groups of type A and B and for affine Artin groups of the same type is given.

Zielgruppe

Research

Autoren/Hrsg.

Callegaro, Filippo

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

1. Coxeter groups and arrangement.- 2. Group cohomology and local systems.- 3. Topology of arrangements.- 4. The integral homology of the Milnor fiber for Artin groups of type A.- 5. The integral homology of the Milnor fiber for Artin groups of type B.- 6. Affine arrangements of type A.- 7. Affine arrangements of type B.