Elliptic Operators Topology And Asymptotic Methods Second Edition PDF Download
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Author | : John Roe |
Publisher | : CRC Press |
Total Pages | : 222 |
Release | : 1999-01-06 |
Genre | : Mathematics |
ISBN | : 9780582325029 |
Download Elliptic Operators, Topology, and Asymptotic Methods, Second Edition Book in PDF, ePub and Kindle
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
Author | : John Roe |
Publisher | : Chapman & Hall/CRC |
Total Pages | : |
Release | : 2017-08-15 |
Genre | : |
ISBN | : 9781138417670 |
Download Elliptic Operators, Topology, and Asymptotic Methods Book in PDF, ePub and Kindle
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
Author | : John Roe |
Publisher | : CRC Press |
Total Pages | : 209 |
Release | : 2013-12-19 |
Genre | : Mathematics |
ISBN | : 1482247836 |
Download Elliptic Operators, Topology, and Asymptotic Methods, Second Edition Book in PDF, ePub and Kindle
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
Author | : John Roe |
Publisher | : Longman Scientific and Technical |
Total Pages | : 208 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : |
Download Elliptic Operators, Topology, and Asymptotic Methods Book in PDF, ePub and Kindle
Author | : Dan Burghelea |
Publisher | : Springer Science & Business Media |
Total Pages | : 312 |
Release | : 2008-03-18 |
Genre | : Mathematics |
ISBN | : 3764386045 |
Download C*-algebras and Elliptic Theory II Book in PDF, ePub and Kindle
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 | : Gerhard Grensing |
Publisher | : World Scientific |
Total Pages | : 1656 |
Release | : 2021-07-15 |
Genre | : Science |
ISBN | : 9811237093 |
Download Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) Book in PDF, ePub and Kindle
The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Author | : Jerome Kaminker |
Publisher | : American Mathematical Soc. |
Total Pages | : 312 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821851128 |
Download Geometric and Topological Invariants of Elliptic Operators Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS-IMS-SIAM Summer Research Conference on ``Geometric and Topological Invariants of Elliptic Operators,'' held in August 1988 at Bowdoin College. Some of the themes covered at the conference and appearing in the articles are: the use of more sophisticated asymptotic methods to obtain index theorems, the study of the $\eta$ invariant and analytic torsion, and index theory on open manifolds and foliated manifolds. The current state of noncommutative differential geometry, as well as operator algebraic and $K$-theoretic methods, are also presented in several the articles. This book will be useful to researchers in index theory, operator algebras, foliations, and mathematical physics. Topologists and geometers are also likely to find useful the view the book provides of recent work in this area. In addition, because of the expository nature of several of the articles, it will be useful to graduate students interested in working in these areas.
Author | : Steven Lord |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 514 |
Release | : 2023-04-03 |
Genre | : Mathematics |
ISBN | : 3110700174 |
Download Trace Formulas Book in PDF, ePub and Kindle
This volume introduces noncommutative integration theory on semifinite von Neumann algebras and the theory of singular traces for symmetric operator spaces. Deeper aspects of the association between measurability, poles and residues of spectral zeta functions, and asymptotics of heat traces are studied. Applications in Connes’ noncommutative geometry that are detailed include integration of quantum differentials, measures on fractals, and Connes’ character formula concerning the Hochschild class of the Chern character.
Author | : A. Comtet |
Publisher | : Springer Science & Business Media |
Total Pages | : 912 |
Release | : 2000-01-20 |
Genre | : Science |
ISBN | : 3540669094 |
Download Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems Book in PDF, ePub and Kindle
Session LXIX. 7 - 31 July 1998
Author | : Piotr Kielanowski |
Publisher | : Birkhäuser |
Total Pages | : 322 |
Release | : 2015-09-21 |
Genre | : Mathematics |
ISBN | : 3319182129 |
Download Geometric Methods in Physics Book in PDF, ePub and Kindle
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.