The Griffiths space and the harmonic archipelago

I recently showed in “The Griffiths double cone group is isomorphic to the triple” (see the arXiv preprint here) that the fundamental group of the Griffiths space is isomorphic to that of the harmonic archipelago. Jeremy Brazas kindly invited me to give a roadmap of the essential ideas through a series of guest posts on his blog. The first of the three posts can be accessed here. Enjoy!

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The nonabelian product modulo sum arXiv:2206.02682
Jonsson groups of various cardinalities, Proc. Amer. Math. Soc. 150 (2022), 2771-2775. arXiv:2101.11035
The Griffiths double cone group is isomorphic to the triple arXiv:2012.06794
A widely connected topological space made from diamond arXiv:2007.10195
Strongly bounded locally indicable groups, Bull. Aust. Math. Soc. 104 (2021), 443-447. (see Theorem C of arXiv:2004.13798 or click here)
Bi-orders do not arise from total orders, Canad. Math. Bull. 65 (2022), 217-224. (see Theorem B of arXiv:2004.13798 or click here.)
The independence of Stone's Theorem from the Boolean Prime Ideal Theorem, Proc. Amer. Math. Soc. 148 (2020), 5381-5386. arXiv:2001.06513
(w/ Olga Varghese) A Nunke type classification in the locally compact setting, J. Algebra 563 (2020), 49-52. arXiv:1912.11867
(w/ Oleg Bogopolski) Abstract homomorphisms from some topological groups to acylindrically hyperbolic groups, to appear in Math. Ann. arXiv:1907.10166
(w/ Saharon Shelah) Strongly bounded groups of various cardinalities, Proc. Amer. Math. Soc. 148 (2020), 5045-5057. arXiv:1906.10481
Freely indecomposable almost free groups with free abelianization, J. Group Theory 23 (2020), 531-543. arXiv:1903.03334
(w/ Ilya Kazachkov) On preservation of automatic continuity, Monatsh. Math. 191 (2020), 37-52.

arXiv:1901.09279
Automatic continuity of aleph_1-free groups, Israel J. Math 237 (2020), 267-285. arXiv:1808.00272
(w/ Saharon Shelah) Deeply concatenable subgroups might never be free, J. Math. Soc. Japan 71 (2019), 1123-1136. arXiv:1804.05538
The number of homomorphisms from the Hawaiian earring group, J. Algebra 523 (2019), 34-52. arXiv:1801.09505
(w/ Wolfram Hojka) The fundamental group of reduced suspensions arXiv:1712.08284
(w/ Greg Conner) A note on automatic continuity, Proc. Amer. Math. Soc. 147 (2019), 1255-1268. arXiv:1710.04787
Root extraction in one-relator groups and slenderness, Comm. in Alg. 46 (2018), 4317-4324. arXiv:1709.02906
Limiting theories of substructures arXiv:1707.08241
On subgroups of first homology, Fund. Math. 247 (2019), 217- 228. arXiv:1610.05422
On definable subgroups of the fundamental group, Topol. Appl 258 (2019), 336-357. arXiv:1610.00145
On quasi-isometry and choice arXiv:1609.01353
Torsion-free word hyperbolic groups are noncommutatively slender, Int. J. Algebra Comput. 26 (2016), 1467-1482. arXiv:1510.04326
(w/ Greg Conner) On the first homology of Peano continua, Fund. Math. 232 (2016), 41-48. arXiv:1509.07055
Subgroups and quotients of fundamental groups (PhD thesis) My PhD Thesis
Applications of descriptive set theory in homotopy theory (MS thesis) My Masters Thesis

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