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2005 The fundamental groups of subsets of closed surfaces inject into their first shape groups
Hanspeter Fischer, Andreas Zastrow
Algebr. Geom. Topol. 5(4): 1655-1676 (2005). DOI: 10.2140/agt.2005.5.1655

Abstract

We show that for every subset X of a closed surface M2 and every x0X, the natural homomorphism φ:π1(X,x0)π̌1(X,x0), from the fundamental group to the first shape homotopy group, is injective. In particular, if XM2 is a proper compact subset, then π1(X,x0) 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.

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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

Information

Received: 7 November 2005; Accepted: 10 November 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1086.55009
MathSciNet: MR2186114
Digital Object Identifier: 10.2140/agt.2005.5.1655

Subjects:
Primary: 55Q07, 55Q52, 57N05
Secondary: 20E25, 20E26

Rights: Copyright © 2005 Mathematical Sciences Publishers

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