LEADER 04244nam 22006135 450 001 9910146272603321 005 20250902193237.0 010 $a3-540-45330-X 024 7 $a10.1007/978-3-540-45330-7 035 $a(CKB)1000000000437264 035 $a(SSID)ssj0000318654 035 $a(PQKBManifestationID)11923600 035 $a(PQKBTitleCode)TC0000318654 035 $a(PQKBWorkID)10310831 035 $a(PQKB)11410565 035 $a(DE-He213)978-3-540-45330-7 035 $a(MiAaPQ)EBC3063651 035 $a(MiAaPQ)EBC6281335 035 $a(PPN)153269995 035 $a(EXLCZ)991000000000437264 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Symplectic Geometry /$fby Ana Cannas da Silva 205 $a1st ed. 2008. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2008. 215 $a1 online resource (XII, 220 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1764 300 $a"ISSN electronic edition 1617-9692." 311 08$a3-540-42195-5 320 $aIncludes bibliographical references (pages [199]-206) and index. 327 $aSymplectic Manifolds -- Symplectic Forms -- Symplectic Form on the Cotangent Bundle -- Symplectomorphisms -- Lagrangian Submanifolds -- Generating Functions -- Recurrence -- Local Forms -- Preparation for the Local Theory -- Moser Theorems -- Darboux-Moser-Weinstein Theory -- Weinstein Tubular Neighborhood Theorem -- Contact Manifolds -- Contact Forms -- Contact Dynamics -- Compatible Almost Complex Structures -- Almost Complex Structures -- Compatible Triples -- Dolbeault Theory -- Kähler Manifolds -- Complex Manifolds -- Kähler Forms -- Compact Kähler Manifolds -- Hamiltonian Mechanics -- Hamiltonian Vector Fields -- Variational Principles -- Legendre Transform -- Moment Maps -- Actions -- Hamiltonian Actions -- Symplectic Reduction -- The Marsden-Weinstein-Meyer Theorem -- Reduction -- Moment Maps Revisited -- Moment Map in Gauge Theory -- Existence and Uniqueness of Moment Maps -- Convexity -- Symplectic Toric Manifolds -- Classification of Symplectic Toric Manifolds -- Delzant Construction -- Duistermaat-Heckman Theorems. 330 $aThe goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1764 606 $aGeometry, Differential 606 $aDifferential equations, Partial 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aGeometry, Differential. 615 0$aDifferential equations, Partial. 615 14$aDifferential Geometry. 615 24$aPartial Differential Equations. 676 $a516.3/6 700 $aSilva$b Ana Cannas da$4aut$4http://id.loc.gov/vocabulary/relators/aut$065988 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146272603321 996 $aLectures on symplectic geometry$9230549 997 $aUNINA