This proof establishes isomorphism between the fundamental groups of the double cone and archipelago groups, suggesting broader implications.
We prove the conjecture of James W. Cannon and Gregory R. Conner that the fundamental group of the Griffiths double cone space is isomorphic to that of the harmonic archipelago. From this and earlier work in this area, we conclude that the isomorphism class of these groups is quite large and includes groups with a great variety of descriptions.
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Samuel M. Corson (2025) studied this question.
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