The fundamental groups of subsets of closed surfaces inject into their first shape groups
by
Hanspeter Fischer
Ball State University
Coauthors: Andreas Zastrow

We show that for every subset X of a closed surface M and every x in X, the natural homomorphism from the fundamental group of X (based at x) to the first shape homotopy group of X (based at x) is injective. In particular, it follows that if X is a proper compact subset of M, then the fundamental group of X (based at x) is isomorphic to a subgroup of the limit of an inverse sequence of finitely generated free groups.

Date received: February 23, 2003