The topological Hawaiian earring group does not embed in the inverse limit of free groups

Fabel, Paul

doi:10.2140/agt.2005.5.1585

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The topological Hawaiian earring group does not embed in the inverse limit of free groups

Paul Fabel

Algebraic & Geometric Topology 5 (2005) 1585–1587

DOI: 10.2140/agt.2005.5.1585

arXiv: math.GN/0501482

Abstract

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.

Keywords

topological fundamental group, inverse limit space, Hawaiian earring

Mathematical Subject Classification 2000

Primary: 57M05, 14F35

Secondary: 54H10, 22A10

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Publication

Received: 15 2005

Revised: 22 October 2005

Accepted: 24 October 2005

Published: 24 November 2005

Authors

Paul Fabel
Drawer MA Department of Mathematics and Statistics Mississippi State University Mississippi State MS 39762 USA

Volume 5, issue 4 (2005)