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Commutator Calculus and Groups of Homotopy Classes (London Mathematical Society Lecture Note Series)
Editorial Reviews ... Product Description | A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic study of the algebraic properties of the classical homotopy operations (composition and addition of maps, smash products, Whitehead products...more
Problems on Mapping Class Groups And Related Topics (Proceedings of Symposia in Pure Mathematics)
Editorial Reviews ... Product Description | The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmüller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into...more
Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Editorial Reviews ... Product Description | This is a collection of articles that grew out of a workshop organized to discuss deep links among various topics that were previously considered unrelated. Rather than a typical workshop, this gathering was unique as it was structured more like a course for advanced graduate students and research mathematicians. In the book, the authors present applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations....more
Mapping Class Groups and Moduli Spaces of Riemann Surfaces: Proceedings of Workshops Held June 24-28, 1991 and August 6-10, 1991 in Gottingen, Germa (Contemporary Mathematics)
Editorial Reviews ... Product Description | The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of Göttingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, this book appeals...more
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (Memoirs of the American Mathematical Society)
Editorial Reviews ... Product Description | The author obtains some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence. In particular, the mapping class groups of different closed surfaces cannot be measure equivalent. Moreover, the author gives various examples of discrete groups which are not measure equivalent to the mapping class groups. In the course of the proof, the author investigates amenability in a measurable sense for the actions of the mapping class group...more
Topics in Hardy Classes and Univalent Functions (Birkhäuser Advanced Texts Basler Lehrbücher)
Editorial Reviews ... Product Description | This book treats classical and contemporary topics in function theory and is accessible after a one-year course in real and complex analysis. It can be used as a text for topics courses or read independently by graduate students and researchers in function theory, operator theory, and applied areas. The first six chapters supplement the authors' book, "Hardy Classes and Operator Theory". The theory of harmonic majorants for subharmonic functions is used to introduce Hardy-Orlicz classes,...more
Differential calculus: For the use of the senior class of Columbia College
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