ON ASYMPTOTIC DIMENSION OF GROUPS ACTING ON TREES G. Bell and A. Dranishnikov
نویسندگان
چکیده
We prove the following. Theorem. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groups Gv having asdimGv ≤ n for all vertices v. Then asdimπ ≤ n + 1. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product.
منابع مشابه
A Hurewicz-type Theorem for Asymptotic Dimension and Applications to Geometric Group Theory
We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finitedimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpo...
متن کاملOn asymptotic dimension of groups
We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdimA ∗C B <∞. B) Suppose that G′ is an HNN extension of a g...
متن کاملN ov 2 00 1 ON ASYMPTOTIC DIMENSION OF GROUPS ACTING ON TREES
We prove the following. Theorem. Let π be the fundamental group of a finite graph of groups with finitely generated vertex groups G v having asdim G v ≤ n for all vertices v. Then asdim π ≤ n + 1. This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product. §0 Introduction The notion of the asymptotic dimension asdim X of a metric space X w...
متن کاملON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS
Abstract. In this paper we show that if G is a group acting on a tree X with inversions and if (T Y ) is a fundamental domain for the action of G on X, then there exist a group &tildeG and a tree &tildeX induced by (T Y ) such that &tildeG acts on &tildeX with inversions, G is isomorphic to &tilde G, and X is isomorphic to &tildeX. The pair (&tilde G &tildeX) is called the quasi universal cover...
متن کاملOn Asymptotic Dimension of Amalgamated Products and Right-angled Coxeter Groups
We prove the inequality asdimA ∗C B ≤ max{asdimA, asdimB, asdimC + 1} under certain conditions on a subgroup C of finitely generated groups A and B. In particular, we prove it for the case when C is normal in A and B. Then we apply this inequality to show that the asymptotic dimension of any right-angled Coxeter group does not exceed the dimension of its Davis’ complex.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002