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Preliminaries

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1629)

Abstract

During the 1980’s, Simon Donaldson utilized the Yang-Mills equations, which had originated in mathematical physics, to study the differential topology of four-manifolds. Using work of Michael Freedman, he was able to prove theorems of the following type:

  1. Theorem A.

    There exist many compact topological four-manifolds which have no smooth structure.

  2. Theorem B.

    There exist many pairs of compact simply connected smooth four-manifolds which are homeomorphic but not diffeomorphic.

Keywords

  • Vector Bundle
  • Line Bundle
  • Cohomology Class
  • Chern Class
  • Local Representative

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). Preliminaries. In: Lectures on Seiberg-Witten Invariants. Lecture Notes in Mathematics, vol 1629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40952-6_1

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  • DOI: https://doi.org/10.1007/978-3-540-40952-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41221-2

  • Online ISBN: 978-3-540-40952-6

  • eBook Packages: Springer Book Archive