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Atiyah Singer Index Theorem An Introduction
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Book Synopsis Atiyah-Singer Index Theorem - An Introduction by : Amiya Mukherjee
Download or read book Atiyah-Singer Index Theorem - An Introduction written by Amiya Mukherjee and published by Hindustan Book Agency. This book was released on 2013-10-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K-theoretic index theorem and its representation in terms of cohomological characteristic classes.
Book Synopsis The Atiyah-Singer Index Theorem by : P. Shanahan
Download or read book The Atiyah-Singer Index Theorem written by P. Shanahan and published by Springer. This book was released on 2006-11-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariance Theory by : Peter B. Gilkey
Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Atiyah-Patodi-Singer Index Theorem by : Richard Melrose
Download or read book The Atiyah-Patodi-Singer Index Theorem written by Richard Melrose and published by CRC Press. This book was released on 1993-03-31 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Seminar on the Atiyah-Singer Index Theorem by : Michael Francis Atiyah
Download or read book Seminar on the Atiyah-Singer Index Theorem written by Michael Francis Atiyah and published by Princeton University Press. This book was released on 1965-09-21 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic treatment of the Atiyah-Singer index theorem from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Book Synopsis Atiyah-Singer Index Theorem - An Introduction by : Amiya Mukherjee
Download or read book Atiyah-Singer Index Theorem - An Introduction written by Amiya Mukherjee and published by Springer. This book was released on 2013-10-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.
Book Synopsis Topology and Analysis by : D.D. Bleecker
Download or read book Topology and Analysis written by D.D. Bleecker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ ent mathematical approaches, and must have experience with their inter connections. The Atiyah-Singer Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrela tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the Atiyah-Singer Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many facetted and always new presentations of the material by M. F.
Book Synopsis Heat Kernels and Dirac Operators by : Nicole Berline
Download or read book Heat Kernels and Dirac Operators written by Nicole Berline and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.
Download or read book Index Theorem. 1 written by M. Furuta and published by American Mathematical Soc.. This book was released on 2007 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Atiyah-Singer index theorem is a remarkable result that allows one to compute the space of solutions of a linear elliptic partial differential operator on a manifold in terms of purely topological data related to the manifold and the symbol of the operator. First proved by Atiyah and Singer in 1963, it marked the beginning of a completely new direction of research in mathematics with relations to differential geometry, partial differential equations, differential topology, K-theory, physics, and other areas.
Book Synopsis The Laplacian on a Riemannian Manifold by : Steven Rosenberg
Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Book Synopsis An Introduction to the Atiyah-Singer Index Theorem by : Patrick Shanahan
Download or read book An Introduction to the Atiyah-Singer Index Theorem written by Patrick Shanahan and published by . This book was released on 1978 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Atiyah-Singer Index Theorem by : P. Shanahan
Download or read book The Atiyah-Singer Index Theorem written by P. Shanahan and published by . This book was released on 2014-01-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 by : Richard S. Palais
Download or read book Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57 written by Richard S. Palais and published by Princeton University Press. This book was released on 2016-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), Volume 57, will be forthcoming.
Book Synopsis The Atiyah-Singer Index Theorem by : Norbert Adasch
Download or read book The Atiyah-Singer Index Theorem written by Norbert Adasch and published by . This book was released on 1978 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elliptic Operators, Topology, and Asymptotic Methods by : John Roe
Download or read book Elliptic Operators, Topology, and Asymptotic Methods written by John Roe and published by Longman Scientific and Technical. This book was released on 1988 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Index Theory with Applications to Mathematics and Physics by : David Bleecker
Download or read book Index Theory with Applications to Mathematics and Physics written by David Bleecker and published by Amer Mathematical Society. This book was released on 2013 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. David Bleecker and Bernhelm Boo�-Bavnbek give two proofs of the Atiyah-Singer Index Theorem in impressive detail: one based on K-theory and the other on the heat kernel approach.
Book Synopsis Differential Geometry for Physicists by : Bo-Yu Hou
Download or read book Differential Geometry for Physicists written by Bo-Yu Hou and published by World Scientific Publishing Company. This book was released on 1997-10-31 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8–10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
