Necessary and sufficient conditions for CW complexes to be homotopy equivalent to total spaces of S^{2k-1}-fibrations over S^{2k}, with order of attaching maps determined and homotopy types classified by stable classes for k not equal to 2 or 4.
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Complexes equivalent to $S^{2k-1}$-fibrations over $S^{2k}$
Necessary and sufficient conditions for CW complexes to be homotopy equivalent to total spaces of S^{2k-1}-fibrations over S^{2k}, with order of attaching maps determined and homotopy types classified by stable classes for k not equal to 2 or 4.