ALL 4-MANIFOLDS HAVE SPINc STRUCTURES PETER TEICHNER AND ELMAR VOGT 1. Introduction The recent developments in the theory of smooth 4-manifolds come from the so-called monopole-equations found by Seiberg and Witten [4].

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• Differential geometry
• Characteristic classes
• Connection
• Cohomology
• StiefelWhitney class
• SeibergWitten invariant
• Manifold
• Torsion tensor
• Orientability
• Differential geometry of surfaces
• Chern class
• Spin structure