The purpose of this article is to describe the integral cohomology of the braid group B3 and SL2 (Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These groups have a description in terms of the so-called ‘divided polynomial algebra’. The results show a strong relation between the torsion part of the computed cohomology and fibrations related to loop spaces of spheres.
THE COHOMOLOGY OF THE BRAID GROUP B3 AND OF SL2(Z) WITH COEFFICIENTS IN A GEOMETRIC REPRESENTATION
CALLEGARO, FILIPPO GIANLUCA;SALVETTI, MARIO
2013-01-01
Abstract
The purpose of this article is to describe the integral cohomology of the braid group B3 and SL2 (Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These groups have a description in terms of the so-called ‘divided polynomial algebra’. The results show a strong relation between the torsion part of the computed cohomology and fibrations related to loop spaces of spheres.File in questo prodotto:
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