AN INDEX THEOREM FOR ELLIPTIC BOUNDARY PROBLEMS. PDF Download
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Author: JOHN JAMES HINRICHSEN
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
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Book Description
Author: JOHN JAMES HINRICHSEN
Publisher:
ISBN:
Category :
Languages : en
Pages : 101
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Book Description
Author: Bernhelm Booß-Bavnbek
Publisher: Springer Science & Business Media
ISBN: 1461203376
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
Author: Stephen Rempel
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 418
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Book Description
Author: Fangbing Wu
Publisher:
ISBN:
Category :
Languages : en
Pages : 160
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Book Description
Author: Stephan Rempel
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311270715X
Category : Mathematics
Languages : en
Pages : 396
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Book Description
No detailed description available for "Index Theory of Elliptic Boundary Problems".
Author: Peter B. Gilkey
Publisher: CRC Press
ISBN: 9780849378744
Category : Mathematics
Languages : en
Pages : 534
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Book Description
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Author: Richard Melrose
Publisher: CRC Press
ISBN: 1439864608
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
Author: Vladimir Nazaikinskii
Publisher: Springer Science & Business Media
ISBN: 3034805101
Category : Mathematics
Languages : en
Pages : 122
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Book Description
The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.
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: Liviu I. Nicolaescu
Publisher: American Mathematical Society(RI)
ISBN: 9781470401948
Category : Geometry, Differential
Languages : en
Pages : 98
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Book Description
In this work, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eight symmetries in the real case and two in the complex case).
