Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Woodhouse, Daniel"'
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete. Notable exa
Externí odkaz:
http://arxiv.org/abs/2303.04843
We exhibit an infinite family of snowflake groups all of whose asymptotic cones are simply connected. Our groups have neither polynomial growth nor quadratic Dehn function, the two usual sources of this phenomenon. We further show that each of our gr
Externí odkaz:
http://arxiv.org/abs/2202.11626
Autor:
Woodhouse, Daniel J.
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 3395-3415
Leighton's graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of non-positively curved special cube complexes that form a natural generalization of regular
Externí odkaz:
http://arxiv.org/abs/2109.03295
Autor:
Shepherd, Sam, Woodhouse, Daniel J.
We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic relative to virtually ab
Externí odkaz:
http://arxiv.org/abs/2007.10034
Autor:
Stark, Emily, Woodhouse, Daniel J.
Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. The Milnor-Schwarz lemma implies that groups with a common model geometry are quasi-isometric; however, the converse
Externí odkaz:
http://arxiv.org/abs/1910.09609
Leighton's graph covering theorem says that two finite graphs with a common cover have a common finite cover. We present a new proof of this using groupoids, and use this as a model to prove two generalisations of the theorem. The first generalisatio
Externí odkaz:
http://arxiv.org/abs/1908.00830
Autor:
Stark, Emily, Woodhouse, Daniel J.
Sela proved every torsion-free one-ended hyperbolic group is coHopfian. We prove that there exist torsion-free one-ended hyperbolic groups that are not commensurably coHopfian. In particular, we show that the fundamental group of every simple surface
Externí odkaz:
http://arxiv.org/abs/1812.07799
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150 (2020) 2937-2951
A tubular group $G$ is a finite graph of groups with $\mathbb{Z}^2$ vertex groups and $\mathbb{Z}$ edge groups. We characterize residually finite tubular groups: $G$ is residually finite if and only if its edge groups are separable. Methods are provi
Externí odkaz:
http://arxiv.org/abs/1811.08098
Autor:
Woodhouse, Daniel J.
Leighton's graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton's theorem that allows generalizations; we prove the corresponding result for graphs
Externí odkaz:
http://arxiv.org/abs/1806.08196
Autor:
Gardam, Giles, Woodhouse, Daniel J.
Publikováno v:
Proc. Amer. Math. Soc. 147 (2019) 125-129
For every pair of positive integers $p > q$ we construct a one-relator group $R_{p,q}$ whose Dehn function is $\simeq n^{2 \alpha}$ where $\alpha = \log_2(2p / q)$. The group $R_{p,q}$ has no subgroup isomorphic to a Baumslag-Solitar group $BS(m,n)$
Externí odkaz:
http://arxiv.org/abs/1711.08755