Author | Mathematical Sciences Research Institute. author |
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Title | Instantons and Four-Manifolds [electronic resource] |
Imprint | New York, NY : Springer New York, 1991 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9703-8 |
Descript | XXI, 194 p. online resource |
to the First Edition -- ยง1 Fake ?4 -- Differentiable structures -- Topological 4-manifolds -- Differentiable 4-manifolds -- A surgical failure -- ยง2 The Yang-Mills Equations -- Connections -- Topological quantum numbers -- The Yang-Mills functional -- Line bundles -- Donaldsonโs Theorem -- ยง3 Manifolds of Connections -- Sobolev spaces -- Reducible connections -- A slice theorem -- The parametrized moduli space -- The moduli space -- ยง4 Cones on ??2 -- Slices again -- Structure of the singular point -- Perturbing the metric -- ยง5 Orientability -- Index bundles -- Components of -- The element โ 1 -- ยง6 Introduction to Taubesโ Theorem -- Instantons on S4 -- A grafting procedure -- Tools from analysis -- Analytic properties of SDYME -- ยง7 Taubesโ Theorem -- Blowing up the metric -- The eigenvalue estimate -- The linearized equation -- Taubesโ projection -- ยง8 Compactness -- Compactness and regularity -- Measuring concentrated curvature -- Compactness in M -- ยง9 The Collar Theorem -- Decay estimates -- Conformal deformations -- Exponential gauges -- Connectivity of the collar -- ยง 10 The Technique of Fintushel and Stern -- The moduli space for SO(3) bundles -- Reducible connections -- Analytic details -- Appendix A The Group of Sobolev Gauge Transformations -- Appendix B The Pontrjagin-Thom Construction -- Appendix C Weitzenbรถck Formulas -- Appendix D The Removability of Singularities -- Appendix E Topological Remarks