The Structure of Groups with a Quasiconvex Hierarchy
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.…
Specifikacia The Structure of Groups with a Quasiconvex Hierarchy
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. 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. 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.
Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on
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