Completing Artin's braid group on infinitely many strands

Abstract

A generalization of the topological fundamental group is developed in order to exhibit a topologically complete braid group containing Artin's braid group on infinitely many strands with respect to the following notion of convergence: A sequence of braids b(n) converges to the trivial braid iff for each M>0 eventually the first M strands of b(n) are trivial.

arXiv comment(15 pages) Corrects mistakes, improves the typesetting, and clarifies some proofs and other constructions in the previous version