Embedding, compression and fiberwise homotopy theory.
by John R. Klein
Wayne State University
klein@math.wsu.edu
This paper establishes a `Cairns-Hirsch' type result for
Poincare embeddings: it gives criteria in the metastable range
for a Poincare embedding M x I ---> X x I
between n-dimensional Poincare spaces to arise from a
Poincare embedding M --> X.
This result has quite a few applications. To mention a few:
1) a Poincare embedding theorem for spheres in the middle dimension.
2) a Poincare analogue of Levine's embedding theorem.
3) a Poincare version of the Whitney embedding theorem (settling a
question of Levitt)
4) the existence of diagonal Poincare embeddings (in the 1-connected case).
Included .eps files:
pic1a-comp.eps
pic2-comp.eps
pic3.eps