The Griffiths double cone group is isomorphic to the triple. (English) Zbl 07818424
Summary: It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if \(\kappa\) is a cardinal such that \(2 \leq \kappa \leq 2^{\aleph_0}\) then the \(\kappa \)-fold cone has the same fundamental group as the double cone. The isomorphisms produced are nonconstructive, and no isomorphism between the fundamental group of the 2- and of the \(\kappa \)-fold cones, with \(2 < \kappa \), can be realized via continuous mappings.
MSC:
| 03E75 | Applications of set theory |
| 20A15 | Applications of logic to group theory |
| 55Q52 | Homotopy groups of special spaces |
| 20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
| 20F34 | Fundamental groups and their automorphisms (group-theoretic aspects) |
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