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Submanifolds of codimension two and homology equivalent manifolds

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

Annales de l'institut Fourier

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.The methods involve some...

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