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The bP-component of a (4n1 - 1)-dimensional homotopy sphere L: E 04 - I =_ bP4,, ?D (CokerJ)4n -1 bounding a spin manifold M is shown to be compu- table in terms of the signature and the decomposable Pontrjagin numbers of M.

A note on the $bP$-component of $(4n-1)$-dimensional homotopy spheres