Описание: The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.
Автор: John Meier Название: Groups, Graphs and Trees ISBN: 0521895456 ISBN-13(EAN): 9780521895453 Издательство: Cambridge Academ Рейтинг: Цена: 12187 р. Наличие на складе: Поставка под заказ.
Описание: Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
Автор: John Meier Название: Groups, Graphs and Trees ISBN: 0521719771 ISBN-13(EAN): 9780521719773 Издательство: Cambridge Academ Рейтинг: Цена: 4929 р. Наличие на складе: Поставка под заказ.
Описание: Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.
Автор: Michael Drmota Название: Random Trees ISBN: 3211753559 ISBN-13(EAN): 9783211753552 Издательство: Springer Рейтинг: Цена: 16169 р. Наличие на складе: Поставка под заказ.
Описание: Trees are a fundamental object in graph theory and combinatorics as well as a basic object for data structures and algorithms in computer science. This book provides an introduction into various aspects of trees in random settings and a systematic treatment of the involved mathematical techniques.
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