A Topological Chern Weil Theory

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A Topological Chern-Weil Theory

Author : Anthony Valiant Phillips
Publisher : American Mathematical Soc.
ISBN 13 : 0821825666
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Topological Chern-Weil Theory by : Anthony Valiant Phillips

Download or read book A Topological Chern-Weil Theory written by Anthony Valiant Phillips and published by American Mathematical Soc.. This book was released on 1993 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the general problem of computing characteristic invariants of principal bundles whose structural group [italic capital]G is a topological group. Under the hypothesis that [italic capital]G has real cohomology finitely generated as an [bold]R-module, we are able to give a completely topological, local method for computing representative cocycles for real characteristic classes; our method applies, for example, to the (homologically) 10-dimensional non-Lie group of Hilton-Roitberg-Stasheff.

Topological Chern-Weil Theory

Author : Anthony Valiant Phillips
Publisher : Oxford University Press, USA
ISBN 13 : 9781470400811
Total Pages : 90 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Topological Chern-Weil Theory by : Anthony Valiant Phillips

Download or read book Topological Chern-Weil Theory written by Anthony Valiant Phillips and published by Oxford University Press, USA. This book was released on 2014-08-31 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work develops a topological analogue of the classical Chern-Weil theory as a method for computing the characteristic classes of principal bundles whose structural group is not necessarily a Lie group, but only a cohomologically finite topological group. Substitutes for the tools of differential geometry, such as the connection and curvature forms, are taken from algebraic topology, using work of Adams, Brown, Eilenberg-Moore, Milgram, Milnor and Stasheff. The result is a synthesis of the algebraic-topological and differential-geometric approaches to characteristic classes. In contrast to the first approach, specific cocycles are used, so as to highlight the influence of local geometry on global topology. In contrast to the second, calculations are carried out at the small scale rather than the infinitesimal; in fact, this work may be viewed as a systematic extension of the observation that curvature is the infinitesimal form of the defect in parallel translation around a rectangle. This book could be used as a text for an advanced graduate course in algebraic topology.

Lectures on Chern-Weil Theory and Witten Deformations

Author : Weiping Zhang
Publisher : World Scientific
ISBN 13 : 9812386580
Total Pages : 131 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Lectures on Chern-Weil Theory and Witten Deformations by : Weiping Zhang

Download or read book Lectures on Chern-Weil Theory and Witten Deformations written by Weiping Zhang and published by World Scientific. This book was released on 2001 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to ShiingOCoshen Chern and Andr(r) Weil, as well as a proof of the GaussOCoBonnetOCoChern theorem based on the MathaiOCoQuillen construction of Thom forms; the second part presents analytic proofs of the Poincar(r)OCoHopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. Contents: ChernOCoWeil Theory for Characteristic Classes; Bott and DuistermaatOCoHeckman Formulas; GaussOCoBonnetOCoChern Theorem; Poincar(r)OCoHopf Index Formula: An Analytic Proof; Morse Inequalities: An Analytic Proof; ThomOCoSmale and Witten Complexes; Atiyah Theorem on Kervaire Semi-characteristic. Readership: Graduate students and researchers in differential geometry, topology and mathematical physics."

Topological Group Cohomology of Lie Groups and Chern-Weil Theory for Compact Symmetric Spaces

Author : Christoph Wockel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (935 download)

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Book Synopsis Topological Group Cohomology of Lie Groups and Chern-Weil Theory for Compact Symmetric Spaces by : Christoph Wockel

Download or read book Topological Group Cohomology of Lie Groups and Chern-Weil Theory for Compact Symmetric Spaces written by Christoph Wockel and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

A topological chern-weil theory

Author : Anthony Phillips
Publisher :
ISBN 13 :
Total Pages : 79 pages
Book Rating : 4.:/5 (878 download)

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Book Synopsis A topological chern-weil theory by : Anthony Phillips

Download or read book A topological chern-weil theory written by Anthony Phillips and published by . This book was released on 1993 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Characteristic Classes

Author : John Willard Milnor
Publisher : Princeton University Press
ISBN 13 : 9780691081229
Total Pages : 342 pages
Book Rating : 4.0/5 (812 download)

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Book Synopsis Characteristic Classes by : John Willard Milnor

Download or read book Characteristic Classes written by John Willard Milnor and published by Princeton University Press. This book was released on 1974 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Geometry of Characteristic Classes

Author : Shigeyuki Morita
Publisher : American Mathematical Soc.
ISBN 13 : 0821821393
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry of Characteristic Classes by : Shigeyuki Morita

Download or read book Geometry of Characteristic Classes written by Shigeyuki Morita and published by American Mathematical Soc.. This book was released on 2001 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristic classes are central to the modern study of the topology and geometry of manifolds. They were first introduced in topology, where, for instance, they could be used to define obstructions to the existence of certain fiber bundles. Characteristic classes were later defined (via the Chern-Weil theory) using connections on vector bundles, thus revealing their geometric side. In the late 1960s new theories arose that described still finer structures. Examples of the so-called secondary characteristic classes came from Chern-Simons invariants, Gelfand-Fuks cohomology, and the characteristic classes of flat bundles. The new techniques are particularly useful for the study of fiber bundles whose structure groups are not finite dimensional. The theory of characteristic classes of surface bundles is perhaps the most developed. Here the special geometry of surfaces allows one to connect this theory to the theory of moduli space of Riemann surfaces, i.e., Teichmüller theory. In this book Morita presents an introduction to the modern theories of characteristic classes.

Berry Phases in Electronic Structure Theory

Author : David Vanderbilt
Publisher : Cambridge University Press
ISBN 13 : 1108661300
Total Pages : 395 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Berry Phases in Electronic Structure Theory by : David Vanderbilt

Download or read book Berry Phases in Electronic Structure Theory written by David Vanderbilt and published by Cambridge University Press. This book was released on 2018-11-01 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.

Unified Field Mechanics Ii: Formulations And Empirical Tests - Proceedings Of The Xth Symposium Honoring Noted French Mathematical Physicist Jean-pierre Vigier

Download Unified Field Mechanics Ii: Formulations And Empirical Tests - Proceedings Of The Xth Symposium Honoring Noted French Mathematical Physicist Jean-pierre Vigier PDF Online Free

Author : Richard L Amoroso
Publisher : World Scientific
ISBN 13 : 9813232056
Total Pages : 652 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Unified Field Mechanics Ii: Formulations And Empirical Tests - Proceedings Of The Xth Symposium Honoring Noted French Mathematical Physicist Jean-pierre Vigier by : Richard L Amoroso

Download or read book Unified Field Mechanics Ii: Formulations And Empirical Tests - Proceedings Of The Xth Symposium Honoring Noted French Mathematical Physicist Jean-pierre Vigier written by Richard L Amoroso and published by World Scientific. This book was released on 2018-01-08 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, recording the 10th international symposium honoring noted French mathematical physicist Jean-Pierre Vigier surveys and continues to develop Unified Field Mechanics (UFM) from the perspective of Multiverse cosmology and Topological Field Theory. UFM represents a developing paradigm shift with many new parameters extending the Standard Model to a 3rd regime of Natural Science beyond Quantum Mechanics. UFM is now experimentally testable, thus putatively able to demonstrate the existence of large-scale additional dimensionality (LSXD), test for QED violating phenomena and surmount the quantum uncertainty principle leading to a new 'Age of Discovery' paling all prior ages in the historical progression: Classical Mechanics (3D) to Quantum Mechanics (4D) and now to the birth of the 3rd regime of UFM in additional dimensionality correlating with M-Theory. Many still consider the Planck-scale as the 'basement of reality'. This could only be considered true under the limitations of the Standard Model. As we methodically enter the new regime a profound understanding of the multiverse and additional dimensionality beckons.

Handbook of Geometry and Topology of Singularities III

Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030957608
Total Pages : 822 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities III by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Basic Algebraic Topology and its Applications

Author : Mahima Ranjan Adhikari
Publisher : Springer
ISBN 13 : 813222843X
Total Pages : 628 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Basic Algebraic Topology and its Applications by : Mahima Ranjan Adhikari

Download or read book Basic Algebraic Topology and its Applications written by Mahima Ranjan Adhikari and published by Springer. This book was released on 2016-09-16 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Infinite Dimensional Groups and Manifolds

Author : Tilmann Wurzbacher
Publisher : Walter de Gruyter
ISBN 13 : 3110200015
Total Pages : 259 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Infinite Dimensional Groups and Manifolds by : Tilmann Wurzbacher

Download or read book Infinite Dimensional Groups and Manifolds written by Tilmann Wurzbacher and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.

Vector fields on Singular Varieties

Author : Jean-Paul Brasselet
Publisher : Springer
ISBN 13 : 3642052053
Total Pages : 242 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Vector fields on Singular Varieties by : Jean-Paul Brasselet

Download or read book Vector fields on Singular Varieties written by Jean-Paul Brasselet and published by Springer. This book was released on 2009-11-28 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many authors have questioned the use of the index of the vector field, and of the Chern classes, if the underlying space becomes singular. This book discusses their explorations within the framework of the obstruction theory and the Chern-Weil theory.

An Index of a Graph with Applications to Knot Theory

Author : Kunio Murasugi
Publisher : American Mathematical Soc.
ISBN 13 : 0821825704
Total Pages : 118 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Index of a Graph with Applications to Knot Theory by : Kunio Murasugi

Download or read book An Index of a Graph with Applications to Knot Theory written by Kunio Murasugi and published by American Mathematical Soc.. This book was released on 1993 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are three chapters to the memoir. The first defines and develops the notion of the index of a graph. The next chapter presents the general application of the graph index to knot theory. The last section is devoted to particular examples, such as determining the braid index of alternating pretzel links. A second result shows that for an alternating knot with Alexander polynomial having leading coefficient less than 4 in absolute value, the braid index is determined by polynomial invariants.

An Extension of the Galois Theory of Grothendieck

Author : André Joyal
Publisher : American Mathematical Soc.
ISBN 13 : 0821823124
Total Pages : 87 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Extension of the Galois Theory of Grothendieck by : André Joyal

Download or read book An Extension of the Galois Theory of Grothendieck written by André Joyal and published by American Mathematical Soc.. This book was released on 1984 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.

Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

Author : Yongsheng Han
Publisher : American Mathematical Soc.
ISBN 13 : 0821825925
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by : Yongsheng Han

Download or read book Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces written by Yongsheng Han and published by American Mathematical Soc.. This book was released on 1994 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$

$Download Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ PDF Online Free$

Author : Mauro Beltrametti
Publisher : American Mathematical Soc.
ISBN 13 : 0821802348
Total Pages : 79 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ by : Mauro Beltrametti

Download or read book Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ written by Mauro Beltrametti and published by American Mathematical Soc.. This book was released on 1995 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.