LEADER 04685nam 22007212 450 001 9910780059403321 005 20151005020621.0 010 $a1-107-12463-8 010 $a1-280-43046-X 010 $a9786610430468 010 $a0-511-17547-7 010 $a0-511-15583-2 010 $a0-511-30404-8 010 $a0-511-54309-3 010 $a0-511-04453-4 035 $a(CKB)111056485655744 035 $a(EBL)202129 035 $a(OCoLC)475916909 035 $a(SSID)ssj0000156036 035 $a(PQKBManifestationID)11946831 035 $a(PQKBTitleCode)TC0000156036 035 $a(PQKBWorkID)10114083 035 $a(PQKB)10270052 035 $a(UkCbUP)CR9780511543098 035 $a(MiAaPQ)EBC202129 035 $a(Au-PeEL)EBL202129 035 $a(CaPaEBR)ebr10006821 035 $a(CaONFJC)MIL43046 035 $a(PPN)145830284 035 $a(EXLCZ)99111056485655744 100 $a20090505d2002|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFloer homology groups in Yang-Mills theory /$fS.K. Donaldson with the assistance of M. Furuta and D. Kotschick$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2002. 215 $a1 online resource (vii, 236 pages) $cdigital, PDF file(s) 225 1 $aCambridge tracts in mathematics ;$v147 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-511-01600-X 311 $a0-521-80803-0 320 $aIncludes bibliographical references (p. 231-233) and index. 327 $tYang-Mills theory over compact manifolds --$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. 330 $aThe concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject. 410 0$aCambridge tracts in mathematics ;$v147. 606 $aYang-Mills theory 606 $aFloer homology 606 $aGeometry, Differential 615 0$aYang-Mills theory. 615 0$aFloer homology. 615 0$aGeometry, Differential. 676 $a530.14/35 700 $aDonaldson$b S. K.$052791 702 $aFuruta$b M. 702 $aKotschick$b D. 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910780059403321 996 $aFloer homology groups in Yang-Mills theory$9377777 997 $aUNINA