3-handle cancellation of 4-dimensional handlebody.

Let $X^4$ be the 4-dimensional 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 3-handle?

(I'm concerning about the Andrews-Curtis conjecture)

edited Jun 13 2011 at 17:41

asked Jun 13 2011 at 17:34

What kind of "change" do you want to allow? For example, do you allow replacing $X$ with a 4-ball? That would do it. – Ryan Budney Jun 13 2011 at 17:49

Are you allowing handle slides? Cancellations? Perhaps more or less? – Ryan Budney Jun 13 2011 at 17:53

Fixing diffeomorphism type. – Topologieee Jun 13 2011 at 17:54

Allowing handle slide and cancellation. – Topologieee Jun 13 2011 at 17:54

A little confused -- is John Smith the same person as Topologieee? – Ryan Budney Jun 13 2011 at 17:57

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