For 3-dim Poincare Conjecture, the assumption is 'simply connected'. 
I am wondering whether simply connectedness assumption in 3-dim implies the same homotopy groups as the 3-sphere?


or If we switch the assumption of 'simply connected' to 'homotopy 3-sphere', would it be easier to proof Poincare Conjecuture.



"homotopy sphere" assumption in Poincare Conjecture
See the fifth paragraph of 


<http://www.math.cornell.edu/~hatcher/Papers/3Msurvey.pdf>


