Geometric group theory is a vibrant subject at the heart of modern mathematics. It is currently enjoying a period of rapid growth and great influence marked by a deepening of its fertile interactions with logic, analysis and large-scale geometry, and striking progress has been made on classical problems at the heart of cohomological group theory. This volume provides the reader with a tour through a selection of the most important trends in the field, including limit groups, quasi-isometric rigidity, non-positive curvature in group theory, and L2-methods in geometry, topology and group theory. Major survey articles exploring recent developments in the field are supported by shorter research papers, which are written in a style that readers approaching the field for the first time will find inviting.
A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. T
This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers
This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in
