Atlas: The fundamental groups of subsets of closed surfaces inject into their first shape groups by Hanspeter Fischer

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Spring Topology and Dynamical Systems Conference 2003
March 20-22, 2003
Texas Tech University
Lubbock, TX, USA

Organizers
Wayne Lewis, Razvan Gelca, Harold Bennett, Carl Seaquist

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