Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Belk, James"'
We show that R. Thompson's group $T$ is a maximal subgroup of the group $V$. The argument provides examples of foundational calculations which arise when expressing elements of $V$ as products of transpositions of basic clopen sets in Cantor space $\
Externí odkaz:
http://arxiv.org/abs/2409.12621
We prove finiteness properties for groups of homeomorphisms that have finitely many "singular points", and we describe the normal structure of such groups. As an application, we prove that every countable abelian group can be embedded into a finitely
Externí odkaz:
http://arxiv.org/abs/2407.03149
Autor:
Belk, James, Matucci, Francesco
We give a short proof that every contracting self-similar group embeds into a finitely presented simple group. In particular, any contracting self-similar group embeds into the corresponding R\"over--Nekrashevych group, and this in turn embeds into o
Externí odkaz:
http://arxiv.org/abs/2405.10234
Autor:
Belk, James, Forrest, Bradley
We develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of "undistorted metrics" that are all quasi-equ
Externí odkaz:
http://arxiv.org/abs/2310.17442
We give a unified and self-contained proof of the Nielsen-Thurston classification theorem from the theory of mapping class groups and Thurston's characterization of rational maps from the theory of complex dynamics (plus various extensions of these).
Externí odkaz:
http://arxiv.org/abs/2309.06993
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 hyperbolic groups satisfy this conjecture, that is, each hyperbolic grou
Externí odkaz:
http://arxiv.org/abs/2309.06224
A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group $G$ has solvable word problem if and only if $G$ can be embedded into a finitely presented simple group. We comment on the history of this conjecture and survey
Externí odkaz:
http://arxiv.org/abs/2306.16356
Autor:
Belk, James, Bleak, Collin
The Boone--Higman conjecture is that every recursively presented group with solvable word problem embeds in a finitely presented simple group. We discuss a brief history of this conjecture and work towards it. Along the way we describe some classes o
Externí odkaz:
http://arxiv.org/abs/2306.14863
Autor:
Belk, James, Stott, Liam
We prove that the "pseudo-$F_4$" group is isomorphic to $F_4$, answering a question of Brin. Both of these groups can be described as fast groups of homeomorphisms of the interval generated by bumps, as introduced by Bleak, Brin, Kassabov, Moore, and
Externí odkaz:
http://arxiv.org/abs/2303.16868
We demonstrate the existence of a piecewise linear homeomorphism $f$ of $\mathbb{R}/\mathbb{Z}$ which maps rationals to rationals, whose slopes are powers of $\frac{2}{3}$, and whose rotation number is $\sqrt{2}-1$. This is achieved by showing that a
Externí odkaz:
http://arxiv.org/abs/2211.05825