The Griffiths double cone group is isomorphic to the triple
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916155967406080 |
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| author | Corson, Samuel M. |
| author_facet | Corson, Samuel M. |
| contents | It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $κ$ is a cardinal such that $2 \leq κ\leq 2^{\aleph_0}$ then the $κ$-fold cone has the same fundamental group as the double cone. The isomorphisms produced are non-constructive, and no isomorphism between the fundamental group of the $2$- and of the $κ$-fold cones, with $2 < κ$, can be realized via continuous mappings. We also prove a conjecture of James W. Cannon and Gregory R. Conner which states that the fundamental group of the Griffiths double cone space is isomorphic to that of the harmonic archipelago. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_06794 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Griffiths double cone group is isomorphic to the triple Corson, Samuel M. Group Theory Algebraic Topology Primary 03E75, 20A15, 55Q52, Secondary 20F10, 20F34 It is shown that the fundamental group of the Griffiths double cone space is isomorphic to that of the triple cone. More generally if $κ$ is a cardinal such that $2 \leq κ\leq 2^{\aleph_0}$ then the $κ$-fold cone has the same fundamental group as the double cone. The isomorphisms produced are non-constructive, and no isomorphism between the fundamental group of the $2$- and of the $κ$-fold cones, with $2 < κ$, can be realized via continuous mappings. We also prove a conjecture of James W. Cannon and Gregory R. Conner which states that the fundamental group of the Griffiths double cone space is isomorphic to that of the harmonic archipelago. |
| title | The Griffiths double cone group is isomorphic to the triple |
| topic | Group Theory Algebraic Topology Primary 03E75, 20A15, 55Q52, Secondary 20F10, 20F34 |
| url | https://arxiv.org/abs/2012.06794 |