Topics in Cyclic Theory

This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.

List of contents

Introduction; 1. Background results; 2. Cyclic cocycles and basic operators; 3. Algebras of operators; 4. GNS algebra; 5. Geometrical examples; 6. The algebra of noncommutative differential forms; 7. Hodge decomposition and the Karoubi operator; 8. Connections; 9. Cocycles for a commutative algebra over a manifold; 10. Cyclic cochains; 11. Cyclic cohomology; 12. Periodic cyclic homology; References; List of symbols; Index of notation; Subject index.

About the author

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.

Summary

Noncommutative geometry combines themes from algebra, analysis and geometry and has many applications to physics. This book focuses on cyclic theory, containing background not found in published papers. It is intended for Ph.D. students in analysis and geometry, and researchers using K-theory, cyclic theory, differential geometry and index theory.

Product details

• Authors: Gordon Blower, Gordon (Lancaster University) Blower, Blower Gordon, Daniel G Quillen, Daniel G. Quillen, Daniel G. (University of Oxford) Quillen, Daniel G. (University of Oxford) Blower Quillen, Quillen Daniel G.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.08.2020
• EAN: 9781108479615
• ISBN: 978-1-108-47961-5
• No. of pages: 328
• Series: London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > General, dictionaries; MATHEMATICS / Topology, Mathematical physics, Differential & Riemannian geometry, Differential and Riemannian geometry