C*-algebras and Elliptic Theory II PDF Download
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Author: Dan Burghelea
Publisher: Springer Science & Business Media
ISBN: 3764386045
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
Author: Dan Burghelea
Publisher: Springer Science & Business Media
ISBN: 3764386045
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
Author: Lawrence C. Washington
Publisher: CRC Press
ISBN: 1420071475
Category : Computers
Languages : en
Pages : 533
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Book Description
Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Author: Michael Atiyah
Publisher: CRC Press
ISBN: 0429973179
Category : Mathematics
Languages : en
Pages : 181
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Book Description
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
Author: J. Coates
Publisher: Springer Science & Business Media
ISBN: 9783540665465
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.
Author: Neculai S. Teleman
Publisher: Springer Nature
ISBN: 3030284336
Category : Mathematics
Languages : en
Pages : 406
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Book Description
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Author: Steven Lord
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110392313
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.
Author: Nora Doll
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111172473
Category : Mathematics
Languages : en
Pages : 460
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Book Description
Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1001
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Book Description
Author: Daniel Alpay
Publisher: Springer Science & Business Media
ISBN: 3764373032
Category : Mathematics
Languages : en
Pages : 323
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Book Description
This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Author: Kevin Costello
Publisher: Cambridge University Press
ISBN: 1316730182
Category : Mathematics
Languages : en
Pages : 418
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Book Description
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.
