000			03557nam a22005175i 4500
001			978-1-4471-5496-9
003			DE-He213
005			20140220082456.0
007			cr nn 008mamaa
008			131128s2014 xxk| s |||| 0|eng d
020			_a9781447154969 _9978-1-4471-5496-9
024	7		_a10.1007/978-1-4471-5496-9 _2doi
050		4	_aQA440-699
072		7	_aPBM _2bicssc
072		7	_aMAT012000 _2bisacsh
082	0	4	_a516 _223
100	1		_aAudin, Michèle. _eauthor.
245	1	0	_aMorse Theory and Floer Homology _h[electronic resource] / _cby Michèle Audin, Mihai Damian.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2014.
300			_aXIV, 596 p. 114 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		_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.
520			_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.
650		0	_aMathematics.
650		0	_aGeometry.
650		0	_aGlobal differential geometry.
650		0	_aAlgebraic topology.
650		0	_aCell aggregation _xMathematics.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
650	2	4	_aDifferential Geometry.
650	2	4	_aAlgebraic Topology.
650	2	4	_aManifolds and Cell Complexes (incl. Diff.Topology).
700	1		_aDamian, Mihai. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447154952
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-5496-9
912			_aZDB-2-SMA
999			_c91898 _d91898