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Author: Spiro Karigiannis
Publisher: Springer Nature
ISBN: 1071605771
Category : Mathematics
Languages : en
Pages : 392
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Book Description
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Author: Spiro Karigiannis
Publisher: Springer Nature
ISBN: 1071605771
Category : Mathematics
Languages : en
Pages : 392
Get Book Here
Book Description
This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Author: Ana Cannas da Silva
Publisher: Springer
ISBN: 354045330X
Category : Mathematics
Languages : en
Pages : 240
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Book Description
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author: Sean Bates
Publisher: American Mathematical Soc.
ISBN: 9780821807989
Category : Mathematics
Languages : en
Pages : 150
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Book Description
These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 9780821838457
Category : Mathematics
Languages : en
Pages : 318
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Book Description
Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).
Author: Benson Farb
Publisher: American Mathematical Soc.
ISBN: 0821838385
Category : Mathematics
Languages : en
Pages : 384
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Book Description
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Author: Daniel Huybrechts
Publisher: Cambridge University Press
ISBN: 1316797252
Category : Mathematics
Languages : en
Pages : 499
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Book Description
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Author: Clay Mathematics Institute. Summer School
Publisher: American Mathematical Soc.
ISBN: 9780821837153
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.
Author: Dmitri Burago
Publisher: American Mathematical Society
ISBN: 1470468530
Category : Mathematics
Languages : en
Pages : 415
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Book Description
“Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.
Author: Andrew Ranicki
Publisher: Oxford University Press
ISBN: 9780198509240
Category : Mathematics
Languages : en
Pages : 396
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Book Description
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
Author: Torsten Asselmeyer-Maluga
Publisher: World Scientific
ISBN: 981024195X
Category : Science
Languages : en
Pages : 339
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Book Description
Many Christians have an easier time being saved by grace than they do living in grace every day. But grace is at the center of the life God calls us to--and reflects the heart of the One who calls.These studies in Grace will help you make the connection between grace as a remote biblical concept and grace as a lifestyle--a reality you experience day in, day out. Through an unfolding study of Psalm 23, you'll learn how God--our Good Shepherd--is for you, how he longs to walk with you through temptation, sorrow, and even deep regret. You'll discover God's desire to make his joy your joy. Throughout, you'll learn how enduring, powerful, and life-affirming God's work in your life can be---and rediscover why it's called amazing grace.Leader's guide included!Grace group sessions are:Living in GraceGrace for RegretsSustaining GraceDelighting in GraceA Legacy of GraceGrace ForeverGrace to Share
