03433nam 2200625 450 991048062420332120170822144311.01-4704-0510-5(CKB)3360000000465088(EBL)3114168(SSID)ssj0000889171(PQKBManifestationID)11549046(PQKBTitleCode)TC0000889171(PQKBWorkID)10867764(PQKB)10444778(MiAaPQ)EBC3114168(PPN)195417933(EXLCZ)99336000000046508820080114h20082008 uy| 0engur|n|---|||||txtccrRank one Higgs bundles and representations of fundamental groups of Riemann surfaces /William M. Goldman, Eugene Z. XiaProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (86 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 904"May 2008, volume 193, number 904 (fourth of 5 numbers)."0-8218-4136-X Includes bibliographical references (pages 67-69).""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""""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""""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""Memoirs of the American Mathematical Society ;no. 904.Surfaces, Deformation ofRiemann surfacesGeometry, DifferentialGeometry, AlgebraicElectronic books.Surfaces, Deformation of.Riemann surfaces.Geometry, Differential.Geometry, Algebraic.516.3/6Goldman William Mark62214Xia Eugene Zhu1963-MiAaPQMiAaPQMiAaPQBOOK9910480624203321Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces2018715UNINA