Finiteness properties for the kernel of the pure motion group of n unlinked loops
by
Alexandra Pettet
University of Chicago

The pure symmetric automorphism group of a free group equals the pure motion group of n unlinked loops in R^3 and contains the pure braid group as a subgroup. The homomorphism between these loop groups induced by forgetting a loop extends the homomorphism between pure braid groups induced by forgetting a puncture. We study the homology of the kernel of the loop homomorphism via its action on a certain subcomplex of Autre Space.

Date received: February 12, 2006