Let $X^4$ be the 4dimensional handlebody with $\partial X=S^3$ and $\pi_i(X)=\pi_i(B^4)$.
Is it true that we can always change $X^4$ with handlebody without 3handle?
(I'm concerning about the AndrewsCurtis conjecture)
Let $X^4$ be the 4dimensional handlebody with $\partial X=S^3$ and $\pi_i(X)=\pi_i(B^4)$. Is it true that we can always change $X^4$ with handlebody without 3handle? (I'm concerning about the AndrewsCurtis conjecture) 

