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Tree Lattices
Hyman Bass, Alexander Lubotzky (Broschiert, Englisch)
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Beschreibung
[UPDATED 6/6/2000] Group 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. This monograph extends this approach to the more general investigation of $X$-lattices $\Gamma$, where $X$ is a locally finite tree and $\Gamma$ is a discrete group of automorphisms of $X$ 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 applications to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems.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 unifrom ones; thus a good deal of attention is given to the construction and study of diverse examples. Some interesting new phenomena are observed here which cannot occur in the case of Lie groups. The fundamental technique is the encoding of tree actions in terms of the corresponding quotient "graph of groups." {\it Tree Lattices} should be a helpful resource to researchers in the field, and may also be used for a graduate course in geometric group theory. 53,49 €
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Technische Daten
Erscheinungsdatum
17.09.2011
Sprache
Englisch
EAN
9781461274131
Herausgeber
Birkhäuser Boston
Serien- oder Bandtitel
Progress in Mathematics
Sonderedition
Nein
Autor
Hyman Bass, Alexander Lubotzky
Seitenanzahl
233
Einbandart
Broschiert
Schlagwörter
Graph, Group theory, Number theory, Sim, Vertex, combinatorics, graph theory, lie groups
Thema-Inhalt
PBM - Geometrie
PBD - Diskrete Mathematik
PBG - Gruppen und Gruppentheorie
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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