# Archipelago groups

@inproceedings{Conner2014ArchipelagoG,
title={Archipelago groups},
author={Gregory R. Conner and Wolfram Hojka and Mark H. Meilstrup},
year={2014}
}
• Published 30 October 2014
• Mathematics
The classical archipelago is a non-contractible subset of R3 which is homeomorphic to a disk except at one non-manifold point. Its fundamental group, A , is the quotient of the topologist’s product of Z, the fundamental group of the shrinking wedge of countably many copies of the circle (the Hawaiian earring), modulo the corresponding free product. We show A is locally free, not indicable, and has the rationals both as a subgroup and a quotient group. Replacing Z with arbitrary groups yields…
18 Citations

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