Topics in Cyclic Theory (London Mathematical Society Student Texts): 97 (London Mathematical Society Student Texts, Series Number 97) - Hardcover

Quillen, Daniel G.; Blower, Gordon

Hardcover

ISBN 10: 1108479618 ISBN 13: 9781108479615

Publisher: Cambridge University Press, 2020

Synopsis

Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on noncommutative differential forms, quasi-free algebras and Chern characters on connections.

About this title

About the Authors

Daniel G. Quillen proved Adam's conjecture in topological K-theory, and Serre's conjecture that all projective modules over a polynomial ring are free. He was awarded the Cole Prize in Algebra and the Fields Medal in 1978. He was Waynflete Professor of Pure Mathematics at the University of Oxford, where he lectured on K-theory and cyclic homology.

Gordon Blower is Professor of Mathematical Analysis at Lancaster University, with interests in random matrices and applications of operator theory. He attended Quillen's lectures on cyclic theory when he was a junior researcher in Oxford.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2020
• Language: English
• ISBN 10: 1108479618
• ISBN 13: 9781108479615
• Binding: Hardcover
• Number of pages: 328