Topics in Groups and Geometry: Growth, Amenability, and Random Walks (Springer Monographs in Mathematics)

Book Details

• Author: Tullio Ceccherini-Silberstein

• Publisher: Springer

• Edition: 1st Edition, 2021

• Binding: Paperback

• ISBN: 9783030881115

• Languages: English

• Package Dimensions: 9.3 x 6.1 x 1.2 inches

About the Book

"Geometric Group Theory: Inspired by Gromov's Work" by Tullio Ceccherini-Silberstein provides an in-depth exposition of key topics in geometric group theory, all linked through the foundational contributions of Mikhail Gromov in the 1980s. The book introduces classical theorems about nilpotent and solvable groups, offers a deep dive into group growth, and explores asymptotic cones. Additionally, it covers essential subjects such as dimension theory, hyperbolic geometry, the Burnside problem, amenability, and random walks on groups.

The author expertly unifies these diverse topics under the umbrella of Gromov’s theorem, which states that finitely generated groups of polynomial growth are virtually nilpotent. This theorem has sparked a fascinating area of research, and this book serves to gather many related results that have been scattered across the literature, many for the first time in book form.

Written for mature undergraduate and graduate students in mathematics, this book offers a clear and accessible introduction to geometric, analytic, and probabilistic aspects of infinite groups. It assumes basic familiarity with group theory and topology and presents the material in a way that bridges abstract theory with practical applications.

Whether you are a student delving into group theory or a researcher seeking an understanding of Gromov-inspired geometric group theory, this book provides an invaluable resource for expanding your knowledge in this dynamic area of mathematics.