| Abstract: |
We demonstrate codimension-\( 1 \) knotting in \( S^4 \) and \( S^1
\times S^3 \). That is, there are \( 3 \)-balls with boundary the
standard \( 2 \)-sphere in \( S^4 \), which are not isotopic rel
boundary to the standard \( 3 \)-ball and there are non separating \(
3 \)-spheres in \( S^1 \times S^3 \) not isotopic to \( \text{pt.}
\times S^3 \). The latter induces diffeomorphisms of \( S^1 \times
S^3 \) that are homotopic to \( \text{id} \) but not isotopic to \(
\text{id} \). (Joint work with Ryan Budney)
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