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Catalogue Information
Field name	Details
Dewey Class	514.74
Title	Smooth Manifolds ([EBook]) / by Claudio Gorodski.
Author	Gorodski, Claudio
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Cham : Springer International Publishing , 2020.
Physical Details	XII, 154 p. 11 illus. : online resource.
Series	Compact Textbooks in Mathematics 2296-4568
ISBN	9783030497750
Summary Note	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. .:
Contents note	Preface -- Smooth manifolds -- Tensor fields and differential forms -- Lie groups -- Integration -- Appendix A: Covering manifolds -- Appendix B: Hodge Theory -- Bibliography -- Index.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-49775-0
Links to Related Works	Subject References: Differential Geometry . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Lie groups . Manifolds (Mathematics) . Topological groups . Authors: author . Gorodski, Claudio . Corporate Authors: SpringerLink (Online service) . Series: Compact Textbooks in Mathematics . Classification: 514.74 .

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Smooth Manifolds

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