Cat(0) Cube Complexes: An Introduction
Schwer, Petra
- 出版商: Springer
- 出版日期: 2024-02-01
- 售價: $2,440
- 貴賓價: 9.5 折 $2,318
- 語言: 英文
- 頁數: 188
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031436210
- ISBN-13: 9783031436215
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商品描述
In recent years cube complexes have become a cornerstone topic of geometric group theory and have proven to be a powerful tool in other areas, such as low dimensional topology, phylogenetic trees or in the context of optimization problems.
This book covers a wide variety of algebraic and geometric properties of cube complexes and the groups acting on them. The content ranges from basic properties of metric spaces, notions of non-positive curvature, Gromov's link condition and the Svarc-Milnor theorem to advanced material such as the cubulation of half-space systems and the Roller boundary, the construction of cube complexes associated with Coxeter groups, and the Tits alternative for cubical groups.
Being the first self-contained, comprehensive introduction to cube complexes this book serves as an entry point for researchers interested in the subject. The material is accessible to advanced undergraduate and graduate students. The text is illustrated with many figures and examples and comes with a large collection of exercises.
This book covers a wide variety of algebraic and geometric properties of cube complexes and the groups acting on them. The content ranges from basic properties of metric spaces, notions of non-positive curvature, Gromov's link condition and the Svarc-Milnor theorem to advanced material such as the cubulation of half-space systems and the Roller boundary, the construction of cube complexes associated with Coxeter groups, and the Tits alternative for cubical groups.
Being the first self-contained, comprehensive introduction to cube complexes this book serves as an entry point for researchers interested in the subject. The material is accessible to advanced undergraduate and graduate students. The text is illustrated with many figures and examples and comes with a large collection of exercises.
商品描述(中文翻譯)
近年來，立方體複合體已成為幾何群論的基石議題，並在其他領域，如低維拓撲學、親緣樹或優化問題的背景下，被證明是一個強大的工具。
本書涵蓋了立方體複合體及其上的群作用的各種代數和幾何性質。內容範圍從度量空間的基本性質、非正曲率的概念、Gromov的鏈條條件和Svarc-Milnor定理，到高級材料，如半空間系統的立方體化和Roller邊界，與Coxeter群相關的立方體複合體的構造，以及立方體群的Tits替代定理。
作為第一本自成一體、全面介紹立方體複合體的書籍，本書為對該主題感興趣的研究人員提供了一個入門點。內容對高年級本科生和研究生來說是可理解的。本文配有許多圖片和例子，並附有大量的練習題。
作者簡介
Petra Schwer is Professor of Mathematics at the Otto-von-Guericke University in Magdeburg, Germany. Prior to her current position she taught at Karlsruhe Institute of Technology (KIT) and Ruprecht-Karls-Universität Heidelberg. Petra Schwer studies the interplay between geometric objects and their symmetries. More specifically she works on topics in geometric group theory, metric geometry and combinatorial group theory and likes to apply these methods to adjacent areas. Her current focus is on non-positively curved groups and spaces, polyhedral complexes, as well as Coxeter groups, (Bruhat-Tits) buildings, and their applications.
作者簡介(中文翻譯)
Petra Schwer是德國馬格德堡的奧托·馮·吉爾克大學的數學教授。在現任職位之前，她曾在卡爾斯魯厄理工學院（KIT）和海德堡大學擔任教職。Petra Schwer研究幾何物體與它們的對稱性之間的相互作用。更具體地說，她在幾何群論、度量幾何和組合群論等領域進行研究，並喜歡將這些方法應用於相關領域。她目前的重點是非正曲率群和空間、多面體複合體，以及Coxeter群（Bruhat-Tits）建築及其應用。
