Displaying similar documents to “Stabilisation, bordism and embedded spheres in 4-manifolds.”

Contact topology and the structure of 5-manifolds with π 1 = ℤ 2

Hansjörg Geiges, Charles B. Thomas (1998)

Annales de l'institut Fourier

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We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 ( M ) = ℤ 2 and second Stiefel-Whitney class equal to zero on H 2 ( M ) . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain ℤ 2 -quotients of  S 2 × S 3 .

Constructing manifolds by homotopy equivalences I. An obstruction to constructing PL-manifolds from homology manifolds

Hajime Sato (1972)

Annales de l'institut Fourier

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We aim at constructing a PL-manifold which is cellularly equivalent to a given homology manifold M n . The main theorem says that there is a unique obstruction element in H n - 4 ( M , ℋ 3 ) , where ℋ 3 is the group of 3-dimensional PL-homology spheres modulo those which are the boundary of an acyclic PL-manifold. If the obstruction is zero and M is compact, we obtain a PL-manifold which is simple homotopy equivalent to M .