- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 13:37:18
7
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=GGD&vol=3&iss=2&update_since=2024-03-28
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
3
2009
2
Most actions on regular trees are almost free
Miklós
Abért
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Yair
Glasner
Ben Gurion University of the Negev, BEER SHEVA, ISRAEL
Random generation, almost free actions, dense subgroups, Galton–Watson processes
Let T be a d-regular tree (d ≥ 3) and A = Aut(T) its automorphism group. Let Γ be the group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of Γ has finitely many fixed points on T.
Group theory and generalizations
Combinatorics
General
199
213
10.4171/GGD/54
http://www.ems-ph.org/doi/10.4171/GGD/54
Linearisation of finite Abelian subgroups of the Cremona group of the plane
Jérémy
Blanc
Universität Basel, BASEL, SWITZERLAND
Birational transformations, fixed curves, linearisation, minimal surfaces
Given a finite Abelian subgroup of the Cremona group of the plane, we provide a way to decide whether it is birationally conjugate to a group of automorphisms of a minimal surface. In particular, we prove that a finite cyclic group of birational transformations of the plane is linearisable if and only if none of its non-trivial elements fix a curve of positive genus. For finite Abelian groups, there exists only one surprising exception, a group isomorphic to ℤ/2ℤ × ℤ/4ℤ, whose non-trivial elements do not fix a curve of positive genus but which is not conjugate to a group of automorphisms of a minimal rational surface. We also give some descriptions of automorphisms (not necessarily of finite order) of del Pezzo surfaces and conic bundles.
Algebraic geometry
General
215
266
10.4171/GGD/55
http://www.ems-ph.org/doi/10.4171/GGD/55
Infinite conjugacy classes in groups acting on trees
Yves
de Cornulier
Université Paris-Sud, ORSAY CEDEX, FRANCE
Amalgams, HNN-extensions, infinite conjugacy classes, FC-center
We characterize amalgams and HNN extensions with infinite conjugacy classes.
Group theory and generalizations
General
267
277
10.4171/GGD/56
http://www.ems-ph.org/doi/10.4171/GGD/56
Examples of buildings constructed via covering spaces
Michael
Davis
Ohio State University, COLUMBUS, UNITED STATES
Building, Coxeter group
Covering space theory is used to construct new examples of buildings.
Group theory and generalizations
General
279
298
10.4171/GGD/57
http://www.ems-ph.org/doi/10.4171/GGD/57
Local similarities and the Haagerup property (with an appendix by Daniel S. Farley)
Bruce
Hughes
Vanderbilt University, NASHVILLE, UNITED STATES
Local similarity, ultrametric space, Haagerup property
A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that these groups have the Haagerup property (that is, they are a-T-menable in the sense of Gromov). The class includes Thompson's groups, which have already been shown to have the Haagerup property by D. S. Farley, as well as many other groups acting on boundaries of trees. A sufficient condition, used in this article, for the Haagerup property is shown in the appendix by D. S. Farley to be equivalent to the well-known property of having a proper action on a space with walls.
Group theory and generalizations
Topological groups, Lie groups
General topology
General
299
315
10.4171/GGD/58
http://www.ems-ph.org/doi/10.4171/GGD/58
Combination of quasiconvex subgroups of relatively hyperbolic groups
Eduardo
Martínez Pedroza
Memorial University of Newfoundland, ST. JOHN'S, CANADA
Relatively hyperbolic group, quasi-convex subgroup, combination theorem, parabolic subgroup
For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 ∗Q1 ∩ Q1 Q2. Our results generalize known combination theorems for quasiconvex subgroups of word hyperbolic groups. Some applications are presented.
Group theory and generalizations
General
317
342
10.4171/GGD/59
http://www.ems-ph.org/doi/10.4171/GGD/59
Low degree bounded cohomology and L2-invariants for negatively curved groups
Andreas
Thom
Technische Universität Dresden, DRESDEN, GERMANY
Hyperbolic group, higher rank lattice, property (T), orbit equivalence, ℓ2-invariants, bounded cohomology
We study the subgroup structure of discrete groups that share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups. We provide strong restrictions on the possible s-normal subgroups of a ‘negatively curved’ group. Another result says that the image of a group, which is boundedly generated by a finite set of amenable subgroups, in a group, which admits a proper quasi-1-cocycle into the regular representation, has to be amenable. These results extend to a certain class of randomorphisms in the sense of Monod.
Topological groups, Lie groups
Measure and integration
Dynamical systems and ergodic theory
General
343
358
10.4171/GGD/60
http://www.ems-ph.org/doi/10.4171/GGD/60