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Topological classification of multiaxial U ( n ) -actions (with an appendix by Jared Bass)

Sylvain CappellShmuel WeinbergerMin Yan — 2015

Journal of the European Mathematical Society

This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological...

Submanifolds of codimension two and homology equivalent manifolds

Sylvain E. CappellJulius 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...

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