Monodromy of fiber-type arrangements and orbit configuration spaces

Details Monodromy of fiber-type arrangements and orbit configuration spaces Monodromy of fiber-type arrangements and orbit configuration spaces

1999-10-22

arxiv.org/abs/math/9910121v1

Forum Math. 13 (2001), 505-530

Mathematics

Geometric Topology

LaTeX, 19 pages with 3 figures

Scientific paper

We prove similar theorems concerning the structure of bundles involving complements of fiber-type hyperplane arrangements and orbit configuration spaces. These results facilitate analysis of the fundamental groups of these spaces, which may be viewed as generalizations of the Artin pure braid group. In particular, we resolve two disparate conjectures. We show that the Whitehead group of the fundamental group of the complement of a fiber-type arrangement is trivial, as conjectured by Aravinda, Farrell, and Rouchon. For the orbit configuration space corresponding to the natural action of a finite cyclic group on the punctured plane, we determine the structure of the Lie algebra associated to the lower central series of the fundamental group. Our results show that this Lie algebra is isomorphic to the module of primitives in the homology of the loop space of a related orbit configuration space, as conjectured by Xicotencatl.

Affiliated with

Also associated with

No associations

Rating

Monodromy of fiber-type arrangements and orbit configuration spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Monodromy of fiber-type arrangements and orbit configuration spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monodromy of fiber-type arrangements and orbit configuration spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-427324