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Proof of Theorem I.38

  • Michèle Audin
  • Ana Cannas da Silva
  • Eugene Lerman
Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Abstract

The rest of the lecture notes will be devoted to a proof of Theorem I.38. Right from the beginning the proof will bifurcate into two cases: the contact manifold B is 3-dimensional and dim B > 3. If dimB = 3 we will argue directly using slices that the orbit spaceB/Gis homeomorphic to a closed interval [0, 1] and then use this to compute the integral cohomology ofB. This will show that B cannot be homeomorphic to \( S^* \mathbb{T}^2 = \mathbb{T}^3 \)

Keywords

Toric Manifold Symplectic Vector Space Nondegenerate Critical Point Slice Representation Homogeneous Vector Bundle 
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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Copyright information

© Springer Basel AG 2003

Authors and Affiliations

  • Michèle Audin
    • 1
  • Ana Cannas da Silva
    • 2
  • Eugene Lerman
    • 3
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et CNRSStrasbourg CedexFrance
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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