000 03117nam a22004815i 4500
001 978-1-4614-1105-5
003 DE-He213
005 20140220083733.0
007 cr nn 008mamaa
008 111201s2011 xxu| s |||| 0|eng d
020 _a9781461411055
_9978-1-4614-1105-5
024 7 _a10.1007/978-1-4614-1105-5
_2doi
050 4 _aQA614-614.97
072 7 _aPBKS
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a514.74
_223
100 1 _aNicolaescu, Liviu.
_eauthor.
245 1 3 _aAn Invitation to Morse Theory
_h[electronic resource] /
_cby Liviu Nicolaescu.
264 1 _aNew York, NY :
_bSpringer New York,
_c2011.
300 _aXVI, 353p. 47 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aPreface -- Notations and Conventions -- 1 Morse Functions -- 2 The Topology of Morse Functions -- 3 Applications -- 4 Morse-Smale Flows and Whitney Stratifications -- 5 Basics of Complex Morse Theory -- 6 Exercises and Solutions -- References -- Index.
520 _aThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory.   This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds.   Some features of the second edition include added applications, such as Morse theory and the curvature of  knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
650 0 _aMathematics.
650 0 _aGlobal analysis.
650 0 _aGlobal differential geometry.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
650 2 4 _aDifferential Geometry.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461411048
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-1105-5
912 _aZDB-2-SMA
999 _c106279
_d106279