Link manifolds and periodicity

Link Manifolds and Periodicity 571

REGULAR O (n)-MANIFOLDS, SUSPENSION OF KNOTS, AND KNOT PERIODICITY

1. Statement of the main results. It will be convenient for us to define an n-knot to be a smooth, connected, oriented, n-dimensional (closed) submanifold IP of S (oriented). If X" is homeomorphic to S, then we call it a spherical knot. All manifolds in this note will be oriented and all constructions we consider will induce canonical orientations. This will be understood and not commented upon...

Link Groups of 4-manifolds

We introduce the notion of a flexible 2 -cell and use it to define invariants – link groups – of 4 -manifolds. Flexible cells combine some features of both surfaces and handlebodies, therefore the link group λ(M) measures certain aspects of the handle structure of a 4 -manifold M . This group is a quotient of the fundamental group, and we construct examples of manifolds M with π1(M) 6= λ(M) . M...

Periodicity and Almost-periodicity

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...