Peculiar unknotting question

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

  1. Blake Winter

    Blake Winter Guest

    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
    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
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