Completing Artin's ordered braid group on infinitely many strands
by
Paul Fabel
Mississippi State University

Artin's braid group on n strands B(n) is the fundamental group of the configuration space consisting of planar sets with precisely n elements. Artin's braid group on infinitely many strands B(\infty) is the direct limit of B(n) taken over monomorphisms from B(n) into B(n+1) which attach a 'trivial strand' to each element of B(n). There is a notable order topology on B(\infty) with respect to which B(\infty) becomes a topological group homeomorphic to the rationals. We will exhibit a complete topological group extending B(\infty).

Date received: February 25, 2003