{"product_id":"9780817641207","title":"Progress in Mathematics","description":"\u003ch1\u003eProgress in Mathematics\u003c\/h1\u003e \u003ch2\u003eBass, H.; Bass, Hyman; Carbone, L.; Lubotzky, Alexander; Lunotzky, A.; Rosenberg, G.; Tits, J.\u003c\/h2\u003e \u003cp\u003e[UPDATED 6\/6\/2000] \nGroup actions on trees furnish a unified geometric way of recasting \nthe chapter of combinatorial group theory dealing with free groups, \namalgams, and HNN extensions. Some of the principal examples arise \nfrom rank one simple Lie groups over a non-archimedean local field \nacting on their Bruhat--Tits trees. In particular this leads to a \npowerful method for studying lattices in such Lie groups. \nThis monograph extends this approach to the more general investigation \nof $X$-lattices $\\Gamma$, where $X$ is a locally finite tree and \n$\\Gamma$ is a discrete group of automorphisms of $X$ of finite \ncovolume.  These \"tree lattices\" are the main object of study. \nSpecial attention is given to both parallels and contrasts with the \ncase of Lie groups.  Beyond the Lie group connection, the theory has \napplications to combinatorics and number theory. \nThe authors present a coherent survey of the results on uniform tree \nlattices, and a (previously unpublished) development of the theory of \nnon-uniform tree lattices, including some fundamental and recently \nproved existence theorems.  Non-uniform tree lattices are much more \ncomplicated than unifrom ones;  thus a good deal of attention is given \nto the construction and study of diverse examples.  Some interesting \nnew phenomena are observed here which cannot occur in the case of Lie \ngroups.  The fundamental technique is the encoding  of tree actions in \nterms of the corresponding quotient \"graph of groups.\" \n{\\it Tree Lattices} should be a helpful resource to researchers in the \nfield, and may also be used for a graduate course in geometric group \ntheory.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2000-11-17\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780817641207\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4612-2098-5\u003c\/p\u003e \u003cp\u003eDimensions: cm xcm\u003c\/p\u003e \u003cp\u003ePages: 233\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":46312111636620,"sku":"9780817641207","price":89.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780817641207.jpg?v=1771518924","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780817641207","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}