By Hyman Bass

ISBN-10: 0817641203

ISBN-13: 9780817641207

Staff activities on bushes provide a unified geometric method of recasting the bankruptcy of combinatorial workforce conception facing unfastened teams, amalgams, and HNN extensions. many of the imperative examples come up from rank one basic Lie teams over a non-archimedean neighborhood box performing on their Bruhat--Tits bushes. particularly this ends up in a strong approach for learning lattices in such Lie teams. This monograph extends this method of the extra normal research of $X$-lattices $\Gamma$, the place $X$ is a in the community finite tree and $\Gamma$ is a discrete staff of automorphisms of $X$ of finite covolume. those "tree lattices" are the most item of analysis. specified cognizance is given to either parallels and contrasts with the case of Lie teams. past the Lie workforce connection, the speculation has purposes to combinatorics and quantity thought. The authors current a coherent survey of the implications on uniform tree lattices, and a (previously unpublished) improvement of the speculation of non-uniform tree lattices, together with a few basic and lately proved lifestyles theorems. Non-uniform tree lattices are even more advanced than unifrom ones; therefore a great deal of recognition is given to the development and research of numerous examples. a few fascinating new phenomena are saw the following which can't ensue in relation to Lie teams. the basic strategy is the encoding of tree activities by way of the corresponding quotient "graph of groups." {\it Tree Lattices} can be a priceless source to researchers within the box, and will even be used for a graduate direction in geometric workforce thought.