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Whitehead returned to England, worked at the Admiralty during the War, then he was appointed to a chair at Oxford. Soon after his return to England he wrote another major work on differential geometry On the Covering of a Complete Space by the Geodesics Through a Point (1935).
Whitehead's interests turned more towards topology and he collaborated with Lefschetz. In this area he is best remembered for his work on homotopy equivalence. He also studied Stiefel manifolds and set up a school of topology at Oxford.
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