LEADER 03433nam 2200625 450 001 9910480624203321 005 20170822144311.0 010 $a1-4704-0510-5 035 $a(CKB)3360000000465088 035 $a(EBL)3114168 035 $a(SSID)ssj0000889171 035 $a(PQKBManifestationID)11549046 035 $a(PQKBTitleCode)TC0000889171 035 $a(PQKBWorkID)10867764 035 $a(PQKB)10444778 035 $a(MiAaPQ)EBC3114168 035 $a(PPN)195417933 035 $a(EXLCZ)993360000000465088 100 $a20080114h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRank one Higgs bundles and representations of fundamental groups of Riemann surfaces /$fWilliam M. Goldman, Eugene Z. Xia 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (86 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 904 300 $a"May 2008, volume 193, number 904 (fourth of 5 numbers)." 311 $a0-8218-4136-X 320 $aIncludes bibliographical references (pages 67-69). 327 $a""Contents""; ""Introduction""; ""1. Equivalences of deformation theories""; ""2. The Betti and de Rham deformation theories and their moduli spaces""; ""2.1. The Betti groupoid""; ""2.2. The de Rham groupoid""; ""2.3. Equivalence of de Rham and Betti groupoids""; ""3. The Dolbeault groupoid""; ""3.1. Holomorphic line bundles""; ""3.2. The moduli spaces""; ""3.3. Geometric structure of the Dolbeault moduli space""; ""4. Equivalence of de Rham and Dolbeault groupoids""; ""4.1. Construction of the equivalence""; ""4.2. Higgs coordinates""; ""4.3. Involutions"" 327 $a""5. Hyperkahler geometry on the moduli space""""5.1. The quaternionic structure""; ""5.2. The Riemannian metric""; ""5.3. Complex-symplectic structure""; ""5.4. Quaternionization""; ""6. The twistor space""; ""6.1. The complex projective line""; ""6.2. The twistor space as a smooth vector bundle""; ""6.3. A holomorphic atlas for the twistor space""; ""6.4. The twistor lines""; ""6.5. The real structure on the twistor space""; ""6.6. Symplectic geometry of the twistor space""; ""6.7. The lattice quotient""; ""6.8. Functions and flows""; ""7. The moduli space and the Riemann period matrix"" 327 $a""7.1. Coordinates for the Betti moduli space""""7.2. Abelian differentials and their periods""; ""7.3. Flat connections""; ""7.4. Higgs fields""; ""7.5. The C*-action in terms of the period matrix""; ""7.6. The C*-action and the real points""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 904. 606 $aSurfaces, Deformation of 606 $aRiemann surfaces 606 $aGeometry, Differential 606 $aGeometry, Algebraic 608 $aElectronic books. 615 0$aSurfaces, Deformation of. 615 0$aRiemann surfaces. 615 0$aGeometry, Differential. 615 0$aGeometry, Algebraic. 676 $a516.3/6 700 $aGoldman$b William Mark$062214 702 $aXia$b Eugene Zhu$f1963- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480624203321 996 $aRank one Higgs bundles and representations of fundamental groups of Riemann surfaces$92018715 997 $aUNINA