Geodesic
The topological Hawaiian earring group does not embed in the inverse limit of free groups
Fabel, Paul1
1Drawer MA, Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1585-1587
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Endowed with natural topologies, the fundamental group of the Hawaiian earring continuously injects into the inverse limit of free groups. This note shows the injection fails to have a continuous inverse. Such a phenomenon was unexpected and appears to contradict results of another author.

DOI : 10.2140/agt.2005.5.1585
Keywords: topological fundamental group, inverse limit space, Hawaiian earring

Fabel, Paul  1

1 Drawer MA, Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA 
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Fabel, Paul. The topological Hawaiian earring group does not embed in the inverse limit of free groups. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1585-1587. doi: 10.2140/agt.2005.5.1585

[1] D K Biss, The topological fundamental group and generalized covering spaces, Topology Appl. 124 (2002) 355

[2] P Fabel, Topological fundamental groups can distinguish spaces with isomorphic homotopy groups, Topology Proc. 30 (2006) 187

[3] J W Morgan, I Morrison, A van Kampen theorem for weak joins, Proc. London Math. Soc. $(3)$ 53 (1986) 562

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