Zeta Functions of Discrete Groups Acting on Trees
نویسندگان
چکیده
منابع مشابه
Zeta Functions of Discrete Groups Acting on Trees
This paper generalizes Bass’ work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree. A zeta function associated to a non-uniform tree...
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This note describes the first example of a group that is amenable, but cannot be obtained by subgroups, quotients, extensions and direct limits from the class of groups locally of subexponential growth. It has a balanced presentation ∆ = 〈b, t| [b, t]b, [[[b, t], b], b]〉. In the proof, I show that ∆ acts transitively on a 3-regular tree, and that Γ = 〈b, b −1 〉 stabilizes a vertex and acts by r...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8600