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008			240724s2017 xx o ||||0 eng d
020			_a9781470440602 _q(electronic bk.)
020			_z9781470422035
035			_a(MiAaPQ)EBC4940246
035			_a(Au-PeEL)EBL4940246
035			_a(CaPaEBR)ebr11421870
035			_a(OCoLC)1000451805
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA665.H64 2017
082	0		_a516.3/6
100	1		_aHofer, H.
245	1	0	_aApplications of Polyfold Theory I : _bThe Polyfolds of Gromov-Witten Theory.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2017.
264		4	_c©2017.
300			_a1 online resource (230 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.248
505	0		_aCover -- Title page -- Chapter 1. Introduction and Main Results -- 1.1. The Space Z of Stable Curves -- 1.2. The Bundle W -- 1.3. Fredholm Theory -- 1.4. The GW-invariants -- Chapter 2. Recollections and Technical Results -- 2.1. Deligne-Mumford type Spaces -- 2.2. Sc-smoothness, Sc-splicings, and Polyfolds -- 2.3. Polyfold Fredholm Sections of Strong Polyfold Bundles -- 2.4. Gluings and Anti-Gluings -- 2.5. Implanting Gluings and Anti-gluings into a Manifold -- 2.6. More Sc-smoothness Results. -- Chapter 3. The Polyfold Structures -- 3.1. Good Uniformizing Families of Stable Curves -- 3.2. Compatibility of Good Uniformizers -- 3.3. Compactness Properties of (\cg,\cg') -- 3.4. The Topology on -- 3.5. The Polyfold Structure on the Space -- 3.6. The Polyfold Structure of the Bundle → -- Chapter 4. The Nonlinear Cauchy-Riemann Operator -- 4.1. Fredholm Sections of Strong Polyfold Bundles -- 4.2. The Cauchy-Riemann Section: Results -- 4.3. Some Technical Results -- 4.4. Regularization and Sc-Smoothness of \ov{∂}_{ } -- 4.5. The Filled Section, Proof of Proposition 4.8 -- 4.6. Proofs of Proposition 4.23 and Proposition 4.25 -- Chapter 5. Appendices -- 5.1. Proof of Theorem 2.56 -- 5.2. Proof of Lemma 3.4 -- 5.3. Linearization of the CR-Operator -- 5.4. Consequences of Elliptic Regularity -- 5.5. Proof of Proposition 4.11 -- 5.6. Banach Algebra Properties -- 5.7. Proof of Proposition 4.12 -- 5.8. Proof of Proposition 4.16 -- 5.9. Proof of Lemma 4.19 -- 5.10. Orientations for Sc-Fredholm Sections -- 5.11. The Canonical Orientation in Gromov-Witten Theory -- Bibliography -- Index -- Back Cover.
520			_aIn this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aSymplectic geometry.
655		4	_aElectronic books.
700	1		_aWysocki, K.
700	1		_aZehnder, E.
776	0	8	_iPrint version: _aHofer, H. _tApplications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory _dProvidence : American Mathematical Society,c2017 _z9781470422035
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4940246 _zClick to View
999			_c128782 _d128782