KRECK-STOLZ INVARIANTS FOR QUATERNIONIC LINE BUNDLES.

We generalise the Kreck-Stolz invariants s₂ and s₃ by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spinmanifolds M of dimension 4k-1 with H³(M;Q) = 0 such that c₂(E) ? H⁴(M) is torsion. The t-invariant classifies closed smooth oriented 2-connected rational homology 7-spheres up to almost-diffeomorphism, that is, diffeomorphism up to a connected sum with an exotic sphere. It also detects exotic homeomorphisms between such manifolds. The t-invariant also gives information about quaternionic line bundles over a fixed manifold, and we use it to give a new proof of a theorem of Feder and Gitler about the values of the second Chern classes of quaternionic line bundles over HP^k. The t-invariant for S^4k-1 is closely related to the Adams e-invariant on the (4k - 5)-stem. [ABSTRACT FROM AUTHOR]