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)


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 \( S^* \mathbb{T}^2 = \mathbb{T}^3 \)


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