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

Download or read book Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces written by F. Dahmani and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: he 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, , and the Cremona group. Other examples can be found among groups acting geometrically on 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.