Geometric and Cohomological Methods in Group Theory
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Geometric and Cohomological Methods in Group Theory
About This Book
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.
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Table of contents
- Cover
- Title
- Copyright
- Contents
- Preface
- List of Participants
- Notes on Selaâs work: Limit groups and Makanin-Razborov diagrams
- Solutions to Bestvina & Feighnâs exercises on limit groups
- L2 Invariants from the algebraic point of view
- Constructing non-positively curved spaces and groups
- Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups
- Hattori-Stallings trace and Euler characteristics for groups
- Groups of small homological dimension and the Atiyah conjecture
- Logarithms and assembly maps on Kn(Zl[G])
- On complete resolutions
- Structure theory for branch groups