Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces write by F. Dahmani. This book was released on 2017-01-18. Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces available in PDF, EPUB and Kindle. 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.
Flexibility of Group Actions on the Circle
Flexibility of Group Actions on the Circle - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Flexibility of Group Actions on the Circle write by Sang-hyun Kim. This book was released on 2019-01-02. Flexibility of Group Actions on the Circle available in PDF, EPUB and Kindle. In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.
Geometric Group Theory
Geometric Group Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Group Theory write by Mladen Bestvina. This book was released on 2014-12-24. Geometric Group Theory available in PDF, EPUB and Kindle. Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
The Cremona Group and Its Subgroups
The Cremona Group and Its Subgroups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Cremona Group and Its Subgroups write by Julie Déserti. This book was released on 2021-04-13. The Cremona Group and Its Subgroups available in PDF, EPUB and Kindle. The goal of this book is to present a portrait of the n n-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions. This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.
Beyond Hyperbolicity
Beyond Hyperbolicity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Beyond Hyperbolicity write by Mark Hagen. This book was released on 2019-07-11. Beyond Hyperbolicity available in PDF, EPUB and Kindle. Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.
