Structure of Groups with a Quasiconvex Hierarchy (eBook)

Daniel T. Wise (Autor)

eBook Download: PDF

2021
376 Seiten
Princeton University Press (Verlag)
978-0-691-21350-7 (ISBN)

Infos

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 that generalizes 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.

Produkt-Details

• Erscheint lt. Verlag: 4.5.2021
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 166 color illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: abelian group • Artin group • automorphism • Basis (linear algebra) • Big O notation • bipartite graph • braid group • C0 • Cartesian Product • CAT(0) • Cayley graph • Characteristic subgroup • circumference • combination • Combinatorial group theory • combinatorial map • commutator • conjugacy class • connectedness • Connected space • convex hull • convex set • Coset • counterexample • Coxeter Group • Curvature • Cyclic group • Degeneracy (mathematics) • Diagram (category theory) • DIAMETER • Dimension • Dimension (vector space) • Disjoint sets • Disjoint union • Disk (mathematics) • Double coset • Dual curve • Dual graph • Ellipse • Embedding • Equation • equivalence class • equivalence relation • Euler characteristic • existential quantification • fiber bundle • finite group • Fundamental domain • fundamental group • Generating set of a group • geometric group theory • Graph of groups • graphs of groups • Gromov • group action • Hierarchies • HNN extension • Homomorphism • Homotopy • Hyperbolic 3-manifold • hyperbolic group • Hyperbolic Groups • hyperplane • Inclusion map • incompressible surface • Induced path • Infimum and supremum • Injective function • Internal and external angles • Intersection (set theory) • Klein Bottle • Lexicographical order • Mathematical Induction • Metric Space • Möbius transformation • Monogon • Nilpotent • Notation • one relator groups • Order of magnitude • pairwise • Parity (mathematics) • partially ordered set • Quasiconvex function • quasi-isometry • Quotient space (topology) • rectangle • Relatively hyperbolic group • relatively hyperbolic groups • Retract • simplicial complex • Simply connected space • small cancellation theory • Special case • Sphere • SUBGROUP • subgroup separability • subsequence • Subset • Summation • Theorem • Thurston • Topological space • Topology • Torsion group • Total order • Tree (data structure) • Triangle group • Trichotomy (mathematics) • virtual haken • virtually • word hyperbolic groups
• ISBN-10: 0-691-21350-X / 069121350X
• ISBN-13: 978-0-691-21350-7 / 9780691213507