Abstract: In this short article we explicitly compute the surgery L-groups, after inverting 2, of the fundamental groups of a large class of complex hyperplane arrangement complements in the complex n-space. This result is obtained using the result from `The isomorphism conjecture in L-theory: poly-free groups and one-relator groups' that the Farrell-Jones Fibered Isomorphism Conjecture in L-theory for the relevant groups is true and then using the combinatorial data associated with the hyperplane arrangement and some generalized homology theory computation. In particular this yields an explicit computation of the surgery groups, modulo 2-torsion, of the classical pure braid groups.

The full article will be available soon.

Updated March 22, 2007.