Orbit configuration spaces associated to discrete subgroups of PSL(2,R)

Kavli Affiliate: Toshitake Kohno

| First 5 Authors: Frederick R. Cohen, Toshitake Kohno, Miguel A. Xicotencatl, ,

| Summary:

The purpose of this article is to analyze several Lie algebras associated to
"orbit configuration spaces" obtained from a group G acting freely, and
properly discontinuously on the upper 1/2-plane H^2. The Lie algebra obtained
from the descending central series for the associated fundamental group is
shown to be isomorphic, up to a regrading, to
(1) the Lie algebra obtained from the higher homotopy groups of "higher
dimensional arrangements" modulo torsion, as well as
(2)the Lie obtained from horizontal chord diagrams for surfaces.
The resulting Lie algebras are similar to those studied in [13, 14, 15, 2, 7,
8, 6]. The structure of a related graded Poisson algebra defined below and
obtained from an analogue of the infinitesimal braid relations parametrized by
G is also addressed.

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