6 papers
A piecewise linear homeomorphism of the circle which is periodic under renormalization
James Belk, James Hyde, Justin Tatch Moore
We demonstrate the existence of a piecewise linear homeomorphism of which maps rationals to rationals, whose slopes are powers of , and who…
Hyperbolic groups satisfy the Boone-Higman conjecture
James Belk, Collin Bleak, Francesco Matucci +1
The 1973 Boone-Higman conjecture predicts that every finitely generated group with solvable word problem embeds in a finitely presented simple group. In this paper, we show that hy…
Compact aspherical solenoids
James Belk, Bradley Forrest
We consider compact, aspherical solenoids obtained as the inverse limit of a system of CW~complexes and covering maps. This includes -adic solenoids, as well as the universal hy…
Progress around the Boone-Higman Conjecture
James Belk, Collin Bleak, Francesco Matucci +1
A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group has solvable word problem if and only if can be embedded into a finitely presented…
The Maximality of in Thompson's group
James Belk, Collin Bleak, Martyn Quick +1
We show that R. Thompson's group is a maximal subgroup of the group . The argument provides examples of foundational calculations which arise when expressing elements of …
Boone-Higman embeddings of and mapping class groups of punctured surfaces
James Belk, Francesco Fournier-Facio, James Hyde +1
We prove that the groups satisfy the Boone-Higman conjecture for all , meaning each embeds in a finitely presented simple group. In fact,…