A generalization of fiber-type arrangements and a new deformation method

Michel Jambu, Stefan Papadima
1998 Topology  
We introduce the hypersolvable class of arrangements which contains the fiber-type ones of [14] , then extend and refine various results concerning the topology of the complement, in its interplay with the combinatorics, to this new class. We prove that the K( , 1) property is combinatorial in the hypersolvable class, along with some other properties conjectured to be related to asphericity in [15] . We describe the structure of the fundamental groups of hypersolvable complements and prove that
more » ... their associated graded Lie algebras are always determined by a minimal combinatorial information. We develop a deformation method for producing fibrations of arrangement spaces and emphasize throughout the role played by the quadratic Orlik-Solomon algebra, a variation on a classical combinatorial theme of [27] . We prove that for hypersolvable arrangements the quadratic Orlik-Solomon algebra is always Koszul and also use it to obtain a generalization of the lower central series formula of [14] .
doi:10.1016/s0040-9383(97)00092-x fatcat:xaarlyl7c5d77lxxcgscrdx33q