Abstract
We show that for every subset of a closed surface and every , the natural homomorphism , from the fundamental group to the first shape homotopy group, is injective. In particular, if is a proper compact subset, then is isomorphic to a subgroup of the limit of an inverse sequence of finitely generated free groups; it is therefore locally free, fully residually free and residually finite.
Citation
Hanspeter Fischer. Andreas Zastrow. "The fundamental groups of subsets of closed surfaces inject into their first shape groups." Algebr. Geom. Topol. 5 (4) 1655 - 1676, 2005. https://doi.org/10.2140/agt.2005.5.1655
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