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The Atiyah-Singer index theorem

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Part of the Aspects of Mathematics book series (ASMA,volume 20)

Abstract

Let X be a compact, differentiable manifold of dimension k,and let E and F be complex C -vector bundles over X of rank m, resp. n. Denote by F the vector space of all C -sections of a bundle, and let D: Г(E) + Г(F) be a ℂ-linear map. Each f ∈ Г(E) can be written over a trivializing neighborhood U of a point xX as f = (f l,..., f m ), where the f i are C-functions over U. In the same way the image g = D(f) can be written locally as g = (g 1,..., g n ).

Keywords

  • Vector Bundle
  • Tangent Bundle
  • Euler Number
  • Euler Class
  • Harmonic Form

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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© 1994 Springer Fachmedien Wiesbaden

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Hirzebruch, F., Berger, T., Jung, R. (1994). The Atiyah-Singer index theorem. In: Manifolds and Modular Forms. Aspects of Mathematics, vol 20. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-10726-2_5

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  • DOI: https://doi.org/10.1007/978-3-663-10726-2_5

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-16414-0

  • Online ISBN: 978-3-663-10726-2

  • eBook Packages: Springer Book Archive