TY  - GEN
T1  - The structure of groups with a quasiconvex hierarchy
T2  - Annals of mathematics studies ;
A1  - Wise, Daniel T., 1971-
LA  - English
PP  - Princeton
PB  - Princeton University Press
YR  - 2021
UL  - https://ebooks.jgu.edu.in/Record/jstor_eba_on1195815511
AB  - "This monograph weaves together fundamentals of Mikhail Leonidovich Gromov's hyperbolic groups with the theory of cube complexes dual to spaces with walls. Many fundamental new ideas and methodologies are presented here for the first time: A cubical small-cancellation theory generalizing ideas from the 1960's, a version of "Dehn Filling" that works in the category of special cube complexes, and a variety of new results about right-angled Artin groups. The book culminates by providing an unexpected new theorem about the nature of hyperbolic groups that are constructible as amalgams. Among the stunning applications, are the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of R.J. Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, the book outlines the author's program towards the resolution of the most important remaining conjectures of William Thurston, and achieves substantial progress in this direction. This monograph, which is richly illustrated with over 100 drawings, will be of interest to graduate students and scholars working in geometry, algebra, and topology. This groundbreaking monograph, intended for the Annals of Math series, lays the mathematical groundwork for the solution of the Thurston-Haken Conjecture, a significant result in geometric group theory. It outlines one of the deepest and most surprising pieces of this result, which also has a variety of other implications for geometric group theory. This work also has applications to low-dimensional topology, and the results in this book have since been used by other mathematicians to provide other important results"--
CN  - QA174.2
SN  - 069121350X
SN  - 9780691213507
SN  - 9780691170442
SN  - 9780691170459
KW  - Hyperbolic groups.
KW  - Group theory.
KW  - Groupes hyperboliques.
KW  - Théorie des groupes.
KW  - MATHEMATICS / Group Theory
KW  - Group theory
KW  - Hyperbolic groups
KW  - CAT(0).
KW  - Gromov.
KW  - Thurston.
KW  - geometric group theory.
KW  - graphs of groups.
KW  - hierarchies.
KW  - hyperbolic groups.
KW  - one relator groups.
KW  - relatively hyperbolic groups.
KW  - small cancellation theory.
KW  - subgroup separability.
KW  - virtual haken.
KW  - word hyperbolic groups.
ER  -