TITLE: Tangent Bundle on S^3
QUESTION [6 upvotes]: how to show T(S^3) isomorphic to S^3 cross R^3? so can I say it for every odd dimension?I have shown it for n=1

REPLY [4 votes]: It does not work for any odd dimension, if I recall correctly it will only work for 1,3 and 7 which correspond to real-division algebras...