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The classical archipelago is a non-contractible subset of 3 which is homeomorphic to a disk except at one non-manifold point. Its fundamental group, , is the quotient of the topologist's product of , the fundamental group of the shrinking wedge of countably many copies of the circle (the Hawaiian earring), modulo the corresponding free product. We show is locally free, not indicable, and has the rationals both as a subgroup and a quotient group. Replacing with arbitrary groups yields the notion of archipelago groups.Surprisingly, every archipelago of countable groups is isomorphic to either ( ) or ( 2 ), the cases where the archipelago is built from circles or projective planes respectively. We conjecture that these two groups are isomorphic and prove that for large enough cardinalities of G i , (G i ) is not isomorphic to either.

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