LEADER 04057nam 2200697Ia 450 001 9910825910603321 005 20200520144314.0 010 $a1-282-19426-7 010 $a9786612194269 010 $a3-11-019797-9 024 7 $a10.1515/9783110197976 035 $a(CKB)1000000000688550 035 $a(EBL)314061 035 $a(OCoLC)236337992 035 $a(SSID)ssj0000122343 035 $a(PQKBManifestationID)11142716 035 $a(PQKBTitleCode)TC0000122343 035 $a(PQKBWorkID)10123464 035 $a(PQKB)10766657 035 $a(MiAaPQ)EBC314061 035 $a(DE-B1597)32310 035 $a(OCoLC)979969284 035 $a(DE-B1597)9783110197976 035 $a(Au-PeEL)EBL314061 035 $a(CaPaEBR)ebr10194856 035 $a(CaONFJC)MIL219426 035 $a(OCoLC)935264247 035 $a(PPN)17549326X 035 $a(EXLCZ)991000000000688550 100 $a20070105d2006 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCircle-valued Morse theory$b[electronic resource] /$fAndrei V. Pajitnov 210 $aBerlin ;$aNew York $cDe Gruyter$dc2006 215 $a1 online resource (464 pages) 225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$v32 300 $aDescription based upon print version of record. 311 $a3-11-015807-8 320 $aIncludes bibliographical references (p. [437]-444) and index. 327 $tFront matter --$tContents --$tPreface --$tIntroduction --$tPart 1. Morse functions and vector fields on manifolds --$tCHAPTER 1. Vector fields and C0 topology --$tCHAPTER 2. Morse functions and their gradients --$tCHAPTER 3. Gradient flows of real-valued Morse functions --$tPart 2. Transversality, handles, Morse complexes --$tCHAPTER 4. The Kupka-Smale transversality theory for gradient flows --$tCHAPTER 5. Handles --$tCHAPTER 6. The Morse complex of a Morse function --$tPart 3. Cellular gradients --$tCHAPTER 7. Condition (C) --$tCHAPTER 8. Cellular gradients are C0-generic --$tCHAPTER 9. Properties of cellular gradients --$tPart 4. Circle-valued Morse maps and Novikov complexes --$tCHAPTER 10. Completions of rings, modules and complexes --$tCHAPTER 11. The Novikov complex of a circle-valued Morse map --$tCHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem --$tCHAPTER 13. Counting closed orbits of the gradient flow --$tCHAPTER 14. Selected topics in the Morse-Novikov theory --$tBackmatter 330 $aIn the early 1920's M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. Circle-valued Morse theory originated from a problem in hydrodynamics studied by S. P. Novikov in the early 1980's. Nowadays, it is a constantly growing field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory of Lagrangian intersections, fibrations of manifolds over the circle, dynamical zeta functions, and the theory of knots and links in the three-dimensional sphere. The aim of the book is to give a systematic treatment of geometric foundations of the subject and recent research results. The book is accessible to first year graduate students specializing in geometry and topology. 410 0$aGruyter studies in mathematics ;$v32. 606 $aMorse theory 606 $aManifolds (Mathematics) 610 $aDifferential geometry. 610 $aMorse theory. 615 0$aMorse theory. 615 0$aManifolds (Mathematics) 676 $a514/.74 686 $aSK 350$2rvk 700 $aPajitnov$b Andrei V$01671300 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825910603321 996 $aCircle-valued Morse theory$94033770 997 $aUNINA