Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces

ISBN-13: 9781470421946 / Angielski

F. Dahmani;V. Guirardel;D. Osin

Opis

The authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, $Out(F_n)$, and the Cremona group. Other examples can be found among groups acting geometrically on $CAT(0)$ spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.

Spis treści

• Introduction
• Main results
• Preliminaries
• Generalizing relative hyperbolicity
• Very rotating families
• Examples
• Dehn filling
• Applications
• Some open problems
• References
• Index.