The need to calculate local system cohomolgy of the complement of an hyperplane arrangement arises in various contexts. Nevertheless until now very few it’s known on the direct computation of such cohomology. In this paper the author describes all generators of the first homology group of braid arrangement giving also a complete description of its first characteristic variety, fulfilling results obtained by D. Cohen and A. Suciu in [7]. Moreover she gives also a complete description of the first characteristic variety in the case of the generalized braid arrangement coming from the dihedral group.

On the Cohomology with local coefficients of Pure Braid Groups

SETTEPANELLA S
2009-01-01

Abstract

The need to calculate local system cohomolgy of the complement of an hyperplane arrangement arises in various contexts. Nevertheless until now very few it’s known on the direct computation of such cohomology. In this paper the author describes all generators of the first homology group of braid arrangement giving also a complete description of its first characteristic variety, fulfilling results obtained by D. Cohen and A. Suciu in [7]. Moreover she gives also a complete description of the first characteristic variety in the case of the generalized braid arrangement coming from the dihedral group.
2009
17
1
211
230
http://www.anstuocmath.ro/volume-xvii-2009-fascicola-1
Coxeter group; cohomology with local coefficients; reflection arrangement; Salvetti’s complex
SETTEPANELLA S
File in questo prodotto:
File Dimensione Formato  
SETTEPANELLA_Ovidius.pdf

Accesso aperto

Tipo di file: PDF EDITORIALE
Dimensione 257.41 kB
Formato Adobe PDF
257.41 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1843778
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact