Title: Braids, trees, and operads
Author: Jack Morava
AMS classification: 55R810, 14N35, 20F36
Address: The Johns Hopkins University
Baltimore 21218 Maryland
e-mail: jack@math.jhu.edu
Abstract: The space of unordered configurations of distinct points
in the plane is aspherical, with Artin's braid group as its fundamental
group. Remarkably enough, the space of ordered configurations of
distinct points on the real projective line, modulo projective equivalence,
has a natural compactification (as a space of equivalence classes of trees)
which is also (by a theorem of Davis, Januszkiewicz, and Scott) aspherical.
The classical braid groups are ubiquitous in modern mathematics, with
applications from the theory of operads to the study of the Galois group
of the rationals. The fundamental groups of these new configuration
spaces are not braid groups, but they have many similar formal properties.
This talk [at the Gdansk conference on algebraic topology 05-06-01] is an
introduction to their study.