Elliptic Operators and Compact Groups PDF Download

Author: M.F. Atiyah
Publisher: Springer
ISBN: 3540378111
Category : Mathematics
Languages : en
Pages : 100

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Author: Michael Francis Atiyah
Publisher:
ISBN:
Category : Elliptic operators
Languages : en
Pages : 93

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Author: John Roe
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 208

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Author: Bernhelm Booß-Bavnbek
Publisher: Springer Science & Business Media
ISBN: 1461203376
Category : Mathematics
Languages : en
Pages : 322

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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: Jerome Kaminker
Publisher: American Mathematical Soc.
ISBN: 0821850776
Category : Mathematics
Languages : en
Pages : 334

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Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.

Author: Michael Atiyah
Publisher: Oxford University Press
ISBN: 9780198532774
Category : Biography & Autobiography
Languages : en
Pages : 632

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This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses index theory.

Author: Michael Atiyah
Publisher: OUP Oxford
ISBN: 0191003476
Category : Mathematics
Languages : en
Pages : 477

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Professor Atiyah is one of the greatest living mathematicians and is renowned in the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still actively involved in the mathematics community. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into seven volumes, with the first five volumes divided thematically and the sixth and seventh arranged by date. This seventh volume in Michael Atiyah's Collected Works contains a selection of his publications between 2002 and 2013, including his work on skyrmions; K-theory and cohomology; geometric models of matter; curvature, cones and characteristic numbers; and reflections on the work of Riemann, Einstein and Bott.

Author: Michael Francis Atiyah
Publisher: Oxford University Press
ISBN: 0199689261
Category : Mathematics
Languages : en
Pages : 477

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Book Description
One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.

Author: J. Baker
Publisher: Springer
ISBN: 3540372628
Category : Mathematics
Languages : en
Pages : 150

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With contributions by numerous experts

Author: A. Cornea
Publisher: Springer
ISBN: 3540380191
Category : Mathematics
Languages : en
Pages : 161

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