{"product_id":"tree-lattices-9781461274131","title":"Tree Lattices","description":"\u003cp\u003e • Author(s): H. Bass\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Logic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eGroup actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a non-archimedean local field acting on their Bruhat--Tits trees. In particular this leads to a powerful method for studying lattices in such Lie groups.\u003c\/p\u003e \u003cp\u003eThis monograph extends this approach to the more general investigation of \u003cem\u003eX\u003c\/em\u003e-lattices G, where \u003cem\u003eX\u003c\/em\u003e-is a locally finite tree and G is a discrete group of automorphisms of \u003cem\u003eX\u003c\/em\u003e of finite covolume. These \"tree lattices\" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has application to combinatorics and number theory.\u003c\/p\u003e \u003cp\u003eThe authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems. Non-uniform tree lattices are much more complicated than uniform ones; thus a good deal of attention is given to the construction and study of diverse examples. The fundamental technique is the encoding of tree action in terms of the corresponding quotient \"graphs of groups.\"\u003c\/p\u003e \u003cp\u003e\u003cem\u003eTree Lattices\u003c\/em\u003e should be a helpful resource to researcher sin the field, and may also be used for a graduate course on geometric methods in group theory.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274505969815,"sku":"9781461274131","price":3639.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781461274131.webp?v=1769280127","url":"https:\/\/atlanticbooks.com\/products\/tree-lattices-9781461274131","provider":"Atlantic Books","version":"1.0","type":"link"}