The Structure of groups with a quasiconvex hierarchy:

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from t...

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Bibliographische Detailangaben
1. Verfasser: Wise, Daniel T. 1971- (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Princeton ; Oxford Princeton University Press [2021]
Schriftenreihe:Annals of mathematics studies Number 209
Schlagworte:
Zusammenfassung:This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory generalizing ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams.The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology
Beschreibung:x, 357 Seiten Illustrationen, Diagramme
ISBN:9780691170442

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