Cohomology of finite and affine type Artin groupsover abelian representation

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 areaffine 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 thecohomology of the Artin groups with coefficients in an abelian representation. In this book a description of this cohomology for Artin groups of type A andB and for affine Artin groups of the same type is given. A resume of several results and costructions on braid cohomology is provided Original results withexplicit cohomology descriptions are given A useful bibliography on braid cohomology INDICE: 1. Coxeter groups and arrangement.- 2. Group cohomology and local systems.- 3. Topology of arrangements.- 4. The integral homology of the Milnorfiber 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.

• ISBN: 978-88-7642-345-1
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 170
• Fecha Publicación: 03/08/2009
• Nº Volúmenes: 1
• Idioma: Inglés