000			03828nam a22003978i 4500
001			CR9780511543098
003			UkCbUP
005			20200124160239.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2002||||enk o ||1 0|eng|d
020			_a9780511543098 (ebook)
020			_z9780521808033 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQC174.52.Y37 _bD66 2002
082	0	0	_a530.14/35 _221
100	1		_aDonaldson, S. K., _eauthor.
245	1	0	_aFloer homology groups in Yang-Mills theory / _cS.K. Donaldson with the assistance of M. Furuta and D. Kotschick.
264		1	_aCambridge : _bCambridge University Press, _c2002.
300			_a1 online resource (vii, 236 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v147
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tYang-Mills theory over compact manifolds -- _tThe case of a compact 4-manifold -- _tTechnical results -- _tManifolds with tubular ends -- _tYang-Mills theory and 3-manifolds -- _tInitial discussion -- _tThe Chern-Simons functional -- _tThe instanton equation -- _tLinear operators -- _tAppendix A: local models -- _tAppendix B: pseudo-holomorphic maps -- _tAppendix C: relations with mechanics -- _tLinear analysis -- _tSeparation of variables -- _tSobolev spaces on tubes -- _tRemarks on other operators -- _tThe addition property -- _tWeighted spaces -- _tFloer's grading function; relation with the Atiyah, Patodi, Singer theory -- _tRefinement of weighted theory -- _tL[superscript p] theory -- _tGauge theory and tubular ends -- _tExponential decay -- _tModuli theory -- _tModuli theory and weighted spaces -- _tGluing instantons -- _tGluing in the reducible case -- _tAppendix A: further analytical results -- _tConvergence in the general case -- _tGluing in the Morse--Bott case -- _tThe Floer homology groups -- _tCompactness properties -- _tFloer's instanton homology groups -- _tIndependence of metric -- _tOrientations -- _tDeforming the equations -- _tTransversality arguments -- _tU(2) and SO(3) connections -- _tFloer homology and 4-manifold invariants -- _tThe conceptual picture -- _tThe straightforward case -- _tReview of invariants for closed 4-manifolds -- _tInvariants for manifolds with boundary and b[superscript +]] 1 -- _tReducible connections and cup products -- _tThe maps D[subscript 1], D[subscript 2] -- _tManifolds with b[superscript +] = 0, 1 -- _tThe case b[superscript +] = 1.
520			_aThe concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
650		0	_aYang-Mills theory.
650		0	_aFloer homology.
650		0	_aGeometry, Differential.
700	1		_aFuruta, M., _eauthor.
700	1		_aKotschick, D., _eauthor.
776	0	8	_iPrint version: _z9780521808033
830		0	_aCambridge tracts in mathematics ; _v147.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543098
999			_c518319 _d518317