Fillings and fittings of unit cotangent bundles of odd-dimensional spheres

We introduce the concept of fittings to symplectic fillings of the unit cotangent bundle of odd-dimensional spheres. Assuming symplectic asphericity we show that all fittings are diffeomorphic to the respective unit co-disc bundle.

Bundle structures on manifolds

This note gives homotopy-theoretic criteria in the metastable range for an (n + l)-manifold with boundary to be diffeomorphic to the total space of an l-disc bundle over a closed n-manifold and for two such structures to be equivalent. The results are similar to some theorems of (8) and the main technique used in the proofs is surgery on a map ((l), pp. 42–46, (7), (10)). All manifolds will be smooth.