Download or read book Vector Fields of Bryant Type for Foliations and Harmonic Morphisms written by Mo Xiaohuan and published by . This book was released on 2001 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird and published by Oxford University Press. This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Download or read book Foliations and the Geometry of 3 Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards written by and published by . This book was released on 2001 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theses on any subject submitted by the academic libraries in the UK and Ireland.
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Download or read book Lie Groups and Geometric Aspects of Isometric Actions written by Marcos M. Alexandrino and published by Springer. This book was released on 2015-05-22 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
Download or read book Riemannian Submersions and Related Topics written by Maria Falcitelli and published by World Scientific. This book was released on 2004 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first-ever systematic introduction to thetheory of Riemannian submersions, which was initiated by BarrettO''Neill and Alfred Gray less than four decades ago. The authorsfocus their attention on classification theorems when the total spaceand the fibres have nice geometric properties.
Download or read book Hamilton s Ricci Flow written by Bennett Chow and published by American Mathematical Society, Science Press. This book was released on 2023-07-13 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.
Download or read book The Ambient Metric written by Charles Fefferman and published by Princeton University Press. This book was released on 2011-11-14 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics are introduced and shown to be equivalent to the ambient formulation. Self-dual Poincaré metrics in four dimensions are considered as a special case, leading to a formal power series proof of LeBrun's collar neighborhood theorem proved originally using twistor methods. Conformal curvature tensors are introduced and their fundamental properties are established. A jet isomorphism theorem is established for conformal geometry, resulting in a representation of the space of jets of conformal structures at a point in terms of conformal curvature tensors. The book concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature, applying results in parabolic invariant theory.
Download or read book Foundations of Differential Geometry Volume 2 written by Shoshichi Kobayashi and published by University of Texas Press. This book was released on 1996-02-22 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
Download or read book Parabolic Geometries I written by Andreas Čap and published by American Mathematical Society. This book was released on 2024-07-29 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures and various types of generic distributions. The characteristic feature of parabolic geometries is an equivalent description by a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie group by a parabolic subgroup). Background on differential geometry, with a view towards Cartan connections, and on semisimple Lie algebras and their representations, which play a crucial role in the theory, is collected in two introductory chapters. The main part discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott–Borel–Weil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The constructions of correspondence spaces and twistor spaces and analogs of the Fefferman construction are presented both in general and in several examples. The last chapter studies Weyl structures, which provide classes of distinguished connections as well as an equivalent description of the Cartan connection in terms of data associated to the underlying geometry. Several applications are discussed throughout the text.
Download or read book Variations on a Theme of Borel written by Shmuel Weinberger and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.
Download or read book The Theory of Spinors written by Élie Cartan and published by Courier Corporation. This book was released on 2012-04-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
Download or read book Algebra Geometry and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren
Download or read book The Topological Classification of Stratified Spaces written by Shmuel Weinberger and published by University of Chicago Press. This book was released on 1994 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Download or read book The Geometry of Filtering written by K. David Elworthy and published by Springer Science & Business Media. This book was released on 2010-11-27 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian structure on the state space. In fact, much of what we discuss is simply about two such operators intertwined by a smooth map, the \projection from the state space to the observations space", and does not involve any stochastic analysis. From the point of view of stochastic processes, our purpose is to present and to study the underlying geometric structure which allows us to perform the ltering in a Markovian framework with the resulting conditional law being that of a Markov process which is time inhomogeneous in general. This geometry is determined by the symbol of the operator on the state space which projects to a symbol on the observation space. The projectible symbol induces a (possibly non-linear and partially de ned) connection which lifts the observation process to the state space and gives a decomposition of the operator on the state space and of the noise. As is standard we can recover the classical ltering theory in which the observations are not usually Markovian by application of the Girsanov- Maruyama-Cameron-Martin Theorem. This structure we have is examined in relation to a number of geometrical topics.
