Proof of Theorem I.38

doi:https://doi.org/10.1007/978-3-0348-8071-8_8

Proof of Theorem I.38

Michèle Audin,Ana Cannas da Silva,Eugene Lerman-2003-01-01-Birkhäuser Basel eBooks

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TL;DRAbstract

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 $$ S^* \mathbb{T}^2 = \mathbb{T}^3 $$

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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

MathematicsManifold (fluid mechanics)Orbit (dynamics)Rest (music)CohomologyPure mathematicsDiscrete mathematicsPhysics

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