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up vote 1 down vote favorite Given the usual surjective homomorphism $ Φ:operatorname{SU}(2)to operatorname{SO}(3)$ that maps a quaternion to a rotation matrix, Does there exist a continuous function $f:operatorname{SO}(3)to operatorname{SU}(2)$ such that $ Phi circ f = operatorname{Id}$ on $operatorname{SO}(3)$ ? If yes, what would be this map be? Thank you general-topology lie-groups smooth-manifolds share | cite | improve this question edited Dec 4 at 19:07 asked Dec 2 at 18:58 kot ...

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