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Progress in Mathematics

Tree Lattices

Authors: Bass, Hyman, Lubotzky, Alexander

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About this book

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 G, where X-is a locally finite tree and G 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 application 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The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems.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 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."

Tree Lattices 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.

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"The book is a helpful resource to researchers in the field and students of geometric methods in group theory."

--Educational Book Review


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $64.99
price for USA in USD
  • ISBN 978-1-4612-2098-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA in USD
Softcover $84.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Tree Lattices
Authors
Series Title
Progress in Mathematics
Series Volume
176
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-2098-5
DOI
10.1007/978-1-4612-2098-5
Hardcover ISBN
978-0-8176-4120-7
Softcover ISBN
978-1-4612-7413-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIII, 233
Topics

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