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＜E-Book＞
Smooth Manifolds / by Claudio Gorodski
(Compact Textbooks in Mathematics. ISSN:2296455X)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2020
Size	XII, 154 p. 11 illus : online resource
Authors	*Gorodski, Claudio author SpringerLink (Online service)
Subjects	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Topological groups LCSH:Lie groups LCSH:Geometry, Differential FREE:Global Analysis and Analysis on Manifolds FREE:Topological Groups and Lie Groups FREE:Differential Geometry
Notes	Preface -- Smooth manifolds -- Tensor fields and differential forms -- Lie groups -- Integration -- Appendix A: Covering manifolds -- Appendix B: Hodge Theory -- Bibliography -- Index This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes’ theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike. HTTP:URL=https://doi.org/10.1007/978-3-030-49775-0

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