Titlebook: Configuration Spaces; Geometry, Combinator A. Bjorner,F. Cohen,M. Salvetti Conference proceedings 2012 Scuola Normale Superiore Pisa 2012 a

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https://doi.org/10.1007/978-981-15-2078-5This article is a short version of a paper which addresses the cohomology of the third braid group and of SL.(ℤ) with coefficients in geometric representations. We give precise statements of the results, some tools and some proofs, avoiding very technical computations here.

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famine

On the structure of spaces of commuting elements in compact Lie groups,In this note we study topological invariants of the spaces of homomorphisms Hom(π, .), where π is a finitely generated abelian group and . is a compact Lie group arising as an arbitrary finite product of the classical groups .(.), .(.) and .(.).

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On the fundamental group of the complement of two real tangent conics and an arbitrary number of reWe compute the simplified presentations of the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the resulting groups turn out to be big.

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Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor,Under a certain condition A we give a construction to calculate the intersection cohomology of a rank one local system on the complement to a hyper-plane-like divisor.

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,The cohomology of the braid group ,, and of ,,(ℤ) with coefficients in a geometric representation,This article is a short version of a paper which addresses the cohomology of the third braid group and of SL.(ℤ) with coefficients in geometric representations. We give precise statements of the results, some tools and some proofs, avoiding very technical computations here.