Geometry, Rigidity, and Group Actions - 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 Geometry, Rigidity, and Group Actions write by Benson Farb. This book was released on 2011-04-15. Geometry, Rigidity, and Group Actions available in PDF, EPUB and Kindle. The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
Geometry, Rigidity, and Group Actions
Geometry, Rigidity, and Group Actions - 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 Geometry, Rigidity, and Group Actions write by Robert J. Zimmer. This book was released on 2011-04-15. Geometry, Rigidity, and Group Actions available in PDF, EPUB and Kindle. The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.
Group Actions in Ergodic Theory, Geometry, and Topology
Group Actions in Ergodic Theory, Geometry, and Topology - 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 Group Actions in Ergodic Theory, Geometry, and Topology write by Robert J. Zimmer. This book was released on 2019-12-23. Group Actions in Ergodic Theory, Geometry, and Topology available in PDF, EPUB and Kindle. Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
Group Actions in Ergodic Theory, Geometry, and Topology
Group Actions in Ergodic Theory, Geometry, and Topology - 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 Group Actions in Ergodic Theory, Geometry, and Topology write by Robert J. Zimmer. This book was released on 2019-12-23. Group Actions in Ergodic Theory, Geometry, and Topology available in PDF, EPUB and Kindle. Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
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 Cornelia Druţu. This book was released on 2018-03-28. Geometric Group Theory available in PDF, EPUB and Kindle. The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
