Codimension one immersions and the Kervaire invariant one problem

Codimension one immersions and the Kervaire invariant one problem

Kervaire Invariant One

Around the year 1960 the theory of surgery was developed as part of a program to classify manifolds of dimension greater than 4. Among the questions it addresses is this: Does every framed cobordism class contain a homotopy sphere? Recall that a framing of a closed smooth manifold is an embedding into Euclidean space together with a trivialization of the normal bundle. A good example is given b...

The Kervaire invariant of immersions

where f2. G is an appropriate cobordism theory of immersed submanifolds of Euclidean space. By generalizing techniques of Browder [2] we shall give necessary and sufficient Adams spectral sequence conditions for an element in t2. G to have nonzero Kervaire invariant. Also we will prove that for every j > 1 there exists a closed, differentiable manifold of dimension 2 ) § together with an immers...

KERVAIRE INVARIANT ONE [ after

Around the year 1960 the theory of surgery was developed as part of a program to classify manifolds of dimension greater than 4. Among the questions it addresses is this: Does every framed cobordism class contain a homotopy sphere? Recall that a framing of a closed smooth manifold is an embedding into Euclidean space together with a trivialization of the normal bundle. A good example is given b...

THE KERVAIRE INVARIANT ONE ELEMENT AND THE DOUBLE TRANSFER-f

The Kervaire invariant one problem has been one of the most fundamental and challenging problems in topology [6,8,9, 18, 19,231. Of course, the pivotal work was [S], which translated the original geometric problem [18, 191 into the problem of the stable homotopy groups of the sphere: Is It; E Ext;“” (2/2,;2/2) a permanent cycle in the Adams spectral sequence of the sphere? The traditional belie...