The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation

Details The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation

2012-04-24

arxiv.org/abs/1204.5390v1

Mathematics

Algebraic Topology

41 pages

Scientific paper

The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(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 torsion part of the computed cohomology and fibrations related to loop spaces of spheres.

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