|
Abstract: We analyze the structure of the fundamental groups of certain orbit configuration spaces. These groups are realized as the generalized pure braid groups associated to certain complex reflection groups (full monomial groups), and may thus be viewed as generalizations of the classical Artin pure braid group. We show that a number of properties of the latter extend to these "pure monomial braid groups." In particular, we show that the Lie algebra associated to the lower central series of a pure monomial braid group is isomorphic to the module of primitives in the homology of the loop space of another orbit configuration space, thereby resolving a conjecture of M. Xicoténcatl.
|
