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Spin geometry on four-manifolds

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

Abstract

The fact that ℝ2 possesses a complex multiplication making it into a field has important applications, leading for example to the theory of Riemann surfaces. Similarly, the quaternion multiplication on ℝ4 has important applications to the geometry of four-manifolds. In four dimensions, quaternions yield a simplification of the theory of spinors (which is presented in full generality in the highly recommended references [25] and [4]).

Keywords

  • Vector Bundle
  • Line Bundle
  • Dirac Operator
  • Clifford Algebra
  • Spin Manifold

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). Spin geometry on four-manifolds. 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_2

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  • DOI: https://doi.org/10.1007/978-3-540-40952-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41221-2

  • Online ISBN: 978-3-540-40952-6

  • eBook Packages: Springer Book Archive