منابع مشابه
Groups, geometry, and rigidity
This mini-course is an introduction to some central themes in geometric group theory and their modern offshoots. One of the earliest and most influential results in the area (in fact a precursor to the field of geometric group theory) is Mostow’s celebrated strong rigidity theorem. This course begins with an “annotated” proof of Mostow’s theorem, using the framework of the proof as a means to i...
متن کاملRigidity of Coxeter Groups and Artin Groups
A Coxeter group is rigid if it cannot be defined by two nonisomorphic diagrams. There have been a number of recent results showing that various classes of Coxeter groups are rigid, and a particularly interesting example of a nonrigid Coxeter group has been given in [17]. We show that this example belongs to a general operation of “diagram twisting”. We show that the Coxeter groups defined by tw...
متن کاملMetric Rigidity of Crystallographic Groups
Consider a finite set of Euclidean motions and ask what kind of conditions are necessary for this set to generate a crystallographic group. We investigate a set of Euclidean motions together with a special concept motivated by real crystalline structures existing in nature, called an essential crystallographic set of isometries. An essential crystallographic set of isometries can be endowed wit...
متن کاملQuasi-isometry rigidity of groups
2 Rigidity of non-uniform rank one lattices 6 2.1 Theorems of Richard Schwartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Finite volume real hyperbolic manifolds . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Proof of Theorem 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملQuasi-isometries and Rigidity of Solvable Groups
In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasiisometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in Sol. We prove analogous results for groups quasi-isometric to R⋉Rn where the semidirect product is defined by a diagonalizable matrix of determinant one with ...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2013
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2012.186