Obstruction Theory in Fiber Spaces.
Obstructions to Embedding and Isotopy in the Metastable Range.
Obstructions to the section problem in a fibration with a weak formal base.
Obstructions to the section problem in fibre bundles.
On non-realization results and conjectures of N. Kuhn
We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod-p singular cohomology of a space, for p a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes’ mapping space theorem. The second (for the prime 2) is based on an analysis of the -1 and -2 columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between...
On the Extension of Certain Maps with Values in Spheres
Let E be an oriented, smooth and closed m-dimensional manifold with m ≥ 2 and V ⊂ E an oriented, connected, smooth and closed (m-2)-dimensional submanifold which is homologous to zero in E. Let be the standard inclusion, where Sⁿ is the n-sphere and n ≥ 3. We prove the following extension result: if is a smooth map, then h extends to a smooth map g: E → Sⁿ transverse to and with . Using this result, we give a new and simpler proof of a theorem of Carlos Biasi related to the ambiental bordism...
On the sharpness of the ... 2 and ... 1 Nielsen numbers.