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.

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.

Lecture Notes on Chern-Simons-Witten Theory

Author : Sen Hu
Publisher : World Scientific
ISBN 13 : 9810239092
Total Pages : 214 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Lecture Notes on Chern-Simons-Witten Theory by : Sen Hu

Download or read book Lecture Notes on Chern-Simons-Witten Theory written by Sen Hu and published by World Scientific. This book was released on 2001 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on lectures on topological quantum field theory given in 1989 at Princeton University by E. Witten, in which he unified several important mathematical works in terms of the Donaldson polynomial, Gromov/Floer homology, and Jones polynomials. Witten explained his three-dimensional construction of Jones polynomials, "an elegant construction of a new polynomial invariant in three-dimensional space" (per the author), via quantization of Chern-Simons gauge theory. Hu (Princeton U.) adds missing details and some new developments in the field. Annotation copyrighted by Book News Inc., Portland, OR.

Lectures on Chern-Weil Theory and Witten Deformations

Author : Weiping Zhang
Publisher : World Scientific
ISBN 13 : 9810246854
Total Pages : 131 pages
Book Rating : 4.8/5 (12 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: Drawn from the acclaimed New Princeton Encyclopedia of Poetry and Poetics, the articles in this concise new reference book provide a complete survey of the poetic history and practice in every major national literature or cultural tradition in the world. As with the parent volume, which has sold over 10,000 copies since it was first published in 1993, the intended audience is general readers, journalists, students, teachers, and researchers. The editor's principle of selection was balance, and his goal was to embrace in a structured and reasoned way the diversity of poetry as it is known across the globe today. In compiling material on 106 cultures in 92 national literatures, the book gives full coverage to Indo-European poetries (all the major Celtic, Slavic, Germanic, and Romance languages, as well as other obscure ones such as Hittite), the ancient middle Eastern poetries (Hebrew, Persian, Sumerian, and Assyro-Babylonian), subcontinental Indian poetries (the widest linguistic diversity), Asian and Pacific poetries (Chinese, Japanese, Korean, Vietnamese, Mongolian, and half a dozen others), continental American poetries (all the modern Western cultures and native Indian in North, Central, and South American regions), and African poetries (ancient and emergent, oral and written).

Geometric and Topological Methods for Quantum Field Theory

Author : Alexander Cardona
Publisher : Cambridge University Press
ISBN 13 : 1107355192
Total Pages : 395 pages
Book Rating : 4.1/5 (73 download)

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Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Alexander Cardona

Download or read book Geometric and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by Cambridge University Press. This book was released on 2013-05-09 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.

From Differential Geometry to Non-commutative Geometry and Topology

Author : Neculai S. Teleman
Publisher : Springer Nature
ISBN 13 : 3030284336
Total Pages : 406 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis From Differential Geometry to Non-commutative Geometry and Topology by : Neculai S. Teleman

Download or read book From Differential Geometry to Non-commutative Geometry and Topology written by Neculai S. Teleman and published by Springer Nature. This book was released on 2019-11-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.

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.

Deformation Theory of Pseudogroup Structures

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821812645
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Deformation Theory of Pseudogroup Structures by : Victor Guillemin

Download or read book Deformation Theory of Pseudogroup Structures written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 1966 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Diagram Cohomology and Isovariant Homotopy Theory

Author : Giora Dula
Publisher : American Mathematical Soc.
ISBN 13 : 0821825895
Total Pages : 97 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Diagram Cohomology and Isovariant Homotopy Theory by : Giora Dula

Download or read book Diagram Cohomology and Isovariant Homotopy Theory written by Giora Dula and published by American Mathematical Soc.. This book was released on 1994 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.

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.

Topology and Condensed Matter Physics

Author : Somendra Mohan Bhattacharjee
Publisher : Springer
ISBN 13 : 9811068410
Total Pages : 519 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Topology and Condensed Matter Physics by : Somendra Mohan Bhattacharjee

Download or read book Topology and Condensed Matter Physics written by Somendra Mohan Bhattacharjee and published by Springer. This book was released on 2017-12-20 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail.

Topology and Geometry of Manifolds

Author : Gordana Matic
Publisher : American Mathematical Soc.
ISBN 13 : 0821835076
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology and Geometry of Manifolds by : Gordana Matic

Download or read book Topology and Geometry of Manifolds written by Gordana Matic and published by American Mathematical Soc.. This book was released on 2003 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.

Lie Groups: Structure, Actions, and Representations

Author : Alan Huckleberry
Publisher : Springer Science & Business Media
ISBN 13 : 1461471931
Total Pages : 422 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Lie Groups: Structure, Actions, and Representations by : Alan Huckleberry

Download or read book Lie Groups: Structure, Actions, and Representations written by Alan Huckleberry and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V. Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Korányi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. Ørsted

The Kinematic Formula in Riemannian Homogeneous Spaces

Author : Ralph Howard
Publisher : American Mathematical Soc.
ISBN 13 : 0821825690
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Kinematic Formula in Riemannian Homogeneous Spaces by : Ralph Howard

Download or read book The Kinematic Formula in Riemannian Homogeneous Spaces written by Ralph Howard and published by American Mathematical Soc.. This book was released on 1993 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.

Subgroup Lattices and Symmetric Functions

Author : Lynne M. Butler
Publisher : American Mathematical Soc.
ISBN 13 : 082182600X
Total Pages : 173 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Subgroup Lattices and Symmetric Functions by : Lynne M. Butler

Download or read book Subgroup Lattices and Symmetric Functions written by Lynne M. Butler and published by American Mathematical Soc.. This book was released on 1994 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.