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Introduction to topological quantum computation par Pachos,, Jiannis K. Publication : Cambridge | New York Cambridge University Press 2012 . x, 206 pages , "Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field"-- 26 cm Date : 2012 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Invariants for homology 3-spheres / par Saveliev,, Nikolai, Publication : Berlin ; | New York : Springer, 2002 . xii, 223 p. : 25 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Lectures on morse homology / par Banyaga, Augustin. Publication : [S.l.] : Springer-Verlag New York Inc., 2004 . 326 p. ; , ReliØ. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Metric structures for riemannian and non-riemannian spaces par Gromov,, Mikhail. Publication : [S.l.] Birkhäuser 2006 . 586 p. ; , This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Modern geometry - methods and applications : part I : the geometry of surfaces, transformation groups, and fields / par Dubrovin, B.A. Publication : [S.l.] : Springer, 1991 . 492 p. ; , This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised. 24 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Plateau's problem par Almgren, Frederick J., Jr. Publication : [S.l.] Amer Mathematical Society 2001 . 88 p. , There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book--or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well. 22 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Selected works of wen-tsun wu par Wu, Wen-Tsun. Publication : [S.l.] World Scientific Publishing Company 2008 . 476 p. , This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career. The book covers Wu s papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel Whitney classes of sphere bundles or differential manifolds, established an imbedding theory with an application to the layout problem of integrated circuits, and introduced the I*-functors which turned the rational homotopy theory created by D Sullivan into algorithmic form. In computer mathematics, he discovered Wu s method of mechanical theorem proving by means of computers, which has been applied to prove and even discover on the computers hundreds of non-trivial theorems in various kinds of elementary and differential geometries. He also discovered a new effective method of polynomial equations solving, which has been used to solve problems raised from the fields of robotics and mechanisms, CAGD, computer vision, theoretic physics, celestial mechanics, and chemical equilibrium computation. Contents: On the Product of Sphere Bundles and the Duality Theorem Modulo Two; On Universal Invariant Forms; The Out-In Complementary Principle; On Chern Numbers of Algebraic Varieties with Arbitrary Singularities; On the Foundation of Algebraic Differential Geometry; On a Finiteness Theorem About Optimization Problems; On Surface-Fitting Problem in CAGD; and other papers. 24 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

SHEAVES ON MANIFOLDS : WITH A SHORT HISTORY "LES DEBUTS DE LA THEORIE DES FAISCEAUX" BY CHRISTIAN HOUZEL / par Kashiwara, Masaki. Publication : [S.l.] : Springer, 1990 . 512 p. ; , From the reviews: This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems. Bull. L.M.S. (1992) 24 cm. Date : 1990 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Surgery on contact 3-manifolds and stein surfaces / par Ozbagci, Burak. Publication : Berlin ; | New York : | Budapest : Springer ; | JĐanos Bolyai Mathematical Society, 2004 . 281 p. : 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Symplectic geometry and topology par Traynor,, Yakov Eliashberg and Lisa. Publication : [S.l.] American Mathematical Society 2006 . 430 p. , Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introduction to Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristics and Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. 25 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

The theory of classes of groups / par Wenbin, Guo. Publication : [S.l.] : Springer, 2001 . 264 p. ; , This book gives a systematic introduction to the theory of classes of groups, including research subjects, major (recent) research achievements, and directions for future research. It clearly and concisely treats a wealth of topics, such as a brief introduction to the fundamental knowledge of group theory; the classical part of the theory of classes of groups covering mainly F-covering subgroups, F-projectors, F-injectors and F-normalisers; local formations; Schunck classes; Fitting classes; properties of local formations; formation constructions of finite groups and related applications; and the algebra of formations. Audience: This volume will be of interest to mathematicians involved in group theory and generalisations, algebras, order, lattices, ordered algebraic structures, general mathematical systems and the mathematics of physics and chemistry. 25 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

The theory of fusion systems an algebraic approach par Craven, David A. Publication : Cambridge | New york Cambridge University Press 2011 . xii, 371 pages , "Fusion systems are a recent development in finite group theory and sit at the intersection of algebra and topology. This book is the first to deal comprehensively with this new and expanding field, taking the reader from the basics of the theory right to the state of the art. Three motivational chapters, indicating the interaction of fusion and fusion systems in group theory, representation theory and topology are followed by six chapters that explore the theory of fusion systems themselves. Starting with the basic definitions, the topics covered include: weakly normal and normal subsystems; morphisms and quotients; saturation theorems; results about control of fusion; and the local theory of fusion systems. At the end there is also a discussion of exotic fusion systems. Designed for use as a text and reference work, this book is suitable for graduate students and experts alike"-- 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Topological and bivariant K-theory par Cuntz, Joachim Publication : Basel | Boston Birkhauser 2007 . xi, 262 pages 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Topological methods in algebraic geometry / par Hirzebruch,, Friedrich. Publication : Berlin ; | New York : Springer, 1995 . ix, 234 p. ; , "Reprint of the 1978 edition." | "Originally published as vol. 131 of the Grundlehren der mathematischen Wissenschaften"--T.p. verso. 24 cm. Date : 1995 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Topological methods in group theory par Geoghegan, Ross Publication : New York Springer 2008 . xiv, 473 pages 25 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Topological quantum field theory and four manifolds par Labastida, Jose Publication : Dordrecht Springer 2005 . 222 p. , The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the recent developments that have led to important applications in the context of the topology of four manifolds. 25 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Topologies on closed and closed convex sets / par Beer,, Gerald Alan. Publication : Dordrecht ; | Boston : Kluwer Academic Publishers, 1993 . xi, 340 p. : 25 cm. Date : 1993 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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