MARC Record from harvard_bibliographic_metadata

LEADER: 02469cam a2200337Ma 4500
001 013143781-X
005 20140910154305.0
008 120214s2011 nyua b 001 0 eng d
020 $a9781461411048
020 $a1461411041
035 0 $aocn778198556
040 $aPAU$cPAU
050 4 $aQA331$b.N53 2011
100 1 $aNicolaescu, Liviu I.
245 13 $aAn invitation to morse theory /$cLiviu Nicolaescu.
250 $a2nd ed.
260 $aNew York, NY :$bSpringer,$cc2011.
300 $axvi, 353 p. :$bill. ;$c23 cm.
490 1 $aUniversitext,$x0172-5939
504 $aIncludes bibliographical references (p. 345-348) and index.
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 $aMorse theory.
650 0 $aCell aggregation$xMathematics.
650 0 $aGlobal analysis.
650 0 $aGlobal differential geometry.
650 0 $aMathematics.
830 0 $aUniversitext.
988 $a20120402
049 $aCLSL
906 $0OCLC