Author : F. Dahmani
Release : 2017-01-18
Genre : Mathematics
Kind : eBook
Book Rating : 941/5 ( reviews)
Book Synopsis Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces by : F. Dahmani
Download or read book Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces written by F. Dahmani. This book was released on 2017-01-18. 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.