LEADER 04152nam 22007575 450 001 9910299975603321 005 20251204103941.0 010 $a1-4471-5496-7 024 7 $a10.1007/978-1-4471-5496-9 035 $a(CKB)3710000000078528 035 $a(EBL)1591889 035 $a(SSID)ssj0001067715 035 $a(PQKBManifestationID)11944726 035 $a(PQKBTitleCode)TC0001067715 035 $a(PQKBWorkID)11091912 035 $a(PQKB)10501001 035 $a(DE-He213)978-1-4471-5496-9 035 $a(MiAaPQ)EBC6311871 035 $a(MiAaPQ)EBC1591889 035 $a(Au-PeEL)EBL1591889 035 $a(CaPaEBR)ebr10983443 035 $a(OCoLC)864875003 035 $a(PPN)17609699X 035 $a(EXLCZ)993710000000078528 100 $a20131128d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMorse Theory and Floer Homology /$fby Michèle Audin, Mihai Damian 205 $a1st ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (595 p.) 225 1 $aUniversitext,$x2191-6675 300 $aDescription based upon print version of record. 311 08$a1-4471-5495-9 327 $aIntroduction to Part I -- Morse Functions -- Pseudo-Gradients -- The Morse Complex -- Morse Homology, Applications -- Introduction to Part II -- What You Need To Know About Symplectic Geometry -- The Arnold Conjecture and the Floer Equation -- The Maslov Index -- Linearization and Transversality -- Spaces of Trajectories -- From Floer To Morse -- Floer Homology: Invariance -- Elliptic Regularity -- Technical Lemmas -- Exercises for the Second Part -- Appendices: What You Need to Know to Read This Book. 330 $aThis book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students. 410 0$aUniversitext,$x2191-6675 606 $aGeometry 606 $aGeometry, Differential 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aGeometry 606 $aDifferential Geometry 606 $aAlgebraic Topology 606 $aManifolds and Cell Complexes 615 0$aGeometry. 615 0$aGeometry, Differential. 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics). 615 14$aGeometry. 615 24$aDifferential Geometry. 615 24$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes. 676 $a514 700 $aAudin$b Miche?le$4aut$4http://id.loc.gov/vocabulary/relators/aut$0350523 702 $aDamian$b Mihai$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299975603321 996 $aMorse Theory and Floer Homology$92503202 997 $aUNINA