arXiv subjects

Owen Baker

Publications and source records attributed to Owen Baker.

4 recordsLinked to original sources

arXiv2019

The Generalized Dehn Property

The Dehn property for a complex is that every non-trivial disk diagram has spurs or shells. It implies a linear isoperimetric inequality. It has been conjectured that the same is true of a more general property which also allows cutcells. We give counterexamples. La propriété Dehn pour un complexe est que chaque diagramme de disque non trivial a des éperons ou des shells. Cela implique une inégalité isopérimétrique linéaire. Il a été supposé qu'il en était de même pour une propriété plus générale qui autorise également les cellules de coupe. Nous présentons des contre-exemples.

math.GR↗

arXiv2019

The Conjugacy Problem for Higman's Group

In 1951, Higman constructed a remarkable group $$H=\left\langle a,b,c,d \, \left| \, b^a = b^2, c^b = c^2, d^c = d^2, a^d = a^2 \right. \right\rangle$$ and used it to produce the first examples of infinite simple groups. By studying fixed points of certain finite state transducers, we show the conjugacy problem in $H$ is decidable (for all inputs). Diekert, Laun and Ushakov have recently shown the word problem in $H$ is solvable in polynomial time, using the power circuit technology of Myasnikov, Ushakov and Won. Building on this work, we show in a strongly generic setting that the conjugacy problem has a $O(n^7)$ polynomial time solution.

math.GR↗

arXiv2018

Cannon-Thurston maps, subgroup distortion, and hyperbolic hydra

There is a family of hyperbolic groups known as hyperbolic hydra which contain heavily distorted free subgroups. We prove the existence of Cannon--Thurston maps (that is, maps of the boundaries induced by subgroup inclusion) for these free subgroups. It is known that Cannon--Thurston maps between hyperbolic space boundaries can exist even in the presence of arbitrarily heavy (even non-recursive) distortion. The hyperbolic hydra examples show that Cannon--Thurston maps can exist even between hyperbolic group boundaries in the presence of arbitrarily heavy primitive recursive distortion.

math.GR↗

arXiv2013

Cannon-Thurston maps do not always exist

We construct an example of a hyperbolic group with a hyperbolic subgroup for which the Cannon-Thurston map does not exist. That is, inclusion does not induce a map of the boundaries.

math.GR↗