The double cone group is isomorphic to the archipelago group

2025/09/15 by Samuel M. Corson, Corson, Samuel M. · 1 citation
Environmental Science · Earth and Planetary Sciences · #Methane Hydrates and Related Phenomena #Geology and Paleoclimatology Research

paper · pdf · doi:10.48550/arxiv.2509.11744

Abstract

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.

Citations

• The nonabelian product modulo sum
• Archipelago groups
• The word problem for some uncountable groups given by countable words

Cited by

• Fundamental groups and descriptive set theory

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• Archipelago groups
• The fundamental group of the harmonic archipelago
• On Double Groups and the Poincaré group
• Making spaces wild (simply-connected case)
• Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds. With appendices by Tobias Hartnick and Ralf Köhl and by Julius Grüning and Ralf Köhl