Geometry and Topology of Manifolds: Surfaces and Beyond - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry and Topology of Manifolds: Surfaces and Beyond write by Vicente Muñoz. This book was released on 2020-10-21. Geometry and Topology of Manifolds: Surfaces and Beyond available in PDF, EPUB and Kindle. This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Introduction to Topological Manifolds
Introduction to Topological Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Topological Manifolds write by John M. Lee. This book was released on 2006-04-06. Introduction to Topological Manifolds available in PDF, EPUB and Kindle. Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Topology and Geometry
Topology and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology and Geometry write by Glen E. Bredon. This book was released on 1993-06-24. Topology and Geometry available in PDF, EPUB and Kindle. This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
An Introduction to Manifolds
An Introduction to Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Manifolds write by Loring W. Tu. This book was released on 2010-10-05. An Introduction to Manifolds available in PDF, EPUB and Kindle. Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Manifolds and Differential Geometry
Manifolds and Differential Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Manifolds and Differential Geometry write by Jeffrey Marc Lee. This book was released on 2009. Manifolds and Differential Geometry available in PDF, EPUB and Kindle. Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
