LEADER 03511nam 22006735 450 001 9910483785203321 005 20251113202229.0 010 $a3-030-49775-5 024 7 $a10.1007/978-3-030-49775-0 035 $a(CKB)4100000011363828 035 $a(DE-He213)978-3-030-49775-0 035 $a(MiAaPQ)EBC6274796 035 $a(Au-PeEL)EBL6274796 035 $a(OCoLC)1195825384 035 $a(PPN)250215772 035 $a(MiAaPQ)EBC30766843 035 $a(Au-PeEL)EBL30766843 035 $a(EXLCZ)994100000011363828 100 $a20200801d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSmooth Manifolds /$fby Claudio Gorodski 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (XII, 154 p. 11 illus.) 225 1 $aCompact Textbooks in Mathematics,$x2296-455X 311 08$a3-030-49774-7 320 $aIncludes bibliographical references and index. 327 $aPreface -- Smooth manifolds -- Tensor fields and differential forms -- Lie groups -- Integration -- Appendix A: Covering manifolds -- Appendix B: Hodge Theory -- Bibliography -- Index. 330 $aThis concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms). It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes? theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike. . 410 0$aCompact Textbooks in Mathematics,$x2296-455X 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aTopological groups 606 $aLie groups 606 $aGeometry, Differential 606 $aGlobal Analysis and Analysis on Manifolds 606 $aTopological Groups and Lie Groups 606 $aDifferential Geometry 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aTopological groups. 615 0$aLie groups. 615 0$aGeometry, Differential. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aTopological Groups and Lie Groups. 615 24$aDifferential Geometry. 676 $a516.07 700 $aGorodski$b Cla´udio$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483785203321 996 $aSmooth Manifolds$91886072 997 $aUNINA