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Displaying similar documents to “Singularities and exotic spheres”

Submanifolds of codimension two and homology equivalent manifolds

Sylvain E. Cappell, Julius L. Shaneson (1973)

Annales de l'institut Fourier

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In this paper new methods of studying codimension two embeddings of manifolds are outlined. Results are stated on geometric periodicity of knot cobordism. The group of local knots of a manifold in a 2-plane bundle is introduced and computed, and applied to C o -close embeddings. General codimension two splitting theorems are discussed, with applications to equivariant knots and knot cobordism. A general existence theorem for P.L. (non-locally flat) embeddings is also given. ...

Cyclic branched coverings and homology 3-spheres with large group actions

Bruno P. Zimmermann (2004)

Fundamenta Mathematicae

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We show that, if the covering involution of a 3-manifold M occurring as the 2-fold branched covering of a knot in the 3-sphere is contained in a finite nonabelian simple group G of diffeomorphisms of M, then M is a homology 3-sphere and G isomorphic to the alternating or dodecahedral group 𝔸₅ ≅ PSL(2,5). An example of such a 3-manifold is the spherical Poincaré sphere. We construct hyperbolic analogues of the Poincaré sphere. We also give examples of hyperbolic ℤ₂-homology 3-spheres...

A set of moves for Johansson representation of 3-manifolds

Rubén Vigara (2006)

Fundamenta Mathematicae

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A Dehn sphere Σ in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The Dehn sphere Σ fills M if it defines a cell decomposition of M. The inverse image in S² of the double curves of Σ is the Johansson diagram of Σ and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson diagram of a filling Dehn sphere of M. Montesinos proved that every closed 3-manifold has a Johansson...