Peculiar unknotting question

Discussion in 'Math Research' started by Blake Winter, May 19, 2009.

1. Blake WinterGuest

Suppose we have a pair (S^n+2, D^n) with the disk as a smooth
submanifold of the sphere. It is well known that by collapsing D, this
can be shown to be unknotted. The possibility of such collapse is
shown by taking a tubular neighborhood. Hence any two disks are
isotopic.
However, what if we require that \partial D be fixed throughout the
isotopy, i.e. we take an isotopy rel boundary? Is it the case that any
two choices (with the same fixed boundary) will be isotopic?

Blake Winter, May 19, 2009