Homotopy types of total spaces of S^{2k-1}-bundles over S^{2k} are classified for 2≤k≤6, with a negative answer to a conjecture for k=4 via new equivalence conditions and attaching map formulas.
Whitehead, Elements of Homotopy Theory, Graduate Texts in Mathematics 61, Springer-Verlag, 1978
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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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Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$
Homotopy types of total spaces of S^{2k-1}-bundles over S^{2k} are classified for 2≤k≤6, with a negative answer to a conjecture for k=4 via new equivalence conditions and attaching map formulas.
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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.