7 problems

Classifications of stable tangle singularities is tractable. The $\sF$-equivalence classes of stable $m$-tangle singularities in codimension $p$ are constructively classifiable, an…

Smooth framed isotopy of tame smooth tangles implies diffeomorphism. Given smooth $m$-tame tangles $f:W\to\mathbb{I}^n$ and $f':W'\to\mathbb{I}^n$, if $f$ and $f'$ are smoothly fra…

Framed homeomorphism of tame smooth tangles implies diffeomorphism. If two tame smooth tangles $W\to\mathbb{I}^n$ and $W'\to\mathbb{I}^n$ are framed stratified homeomorphic, then…

Smooth embeddings are generically tame tangles. Given a closed smooth manifold $W$, the subspace of tame smooth tangles $W\to\mathbb{I}^n$ is dense in the space of all smooth embed…

Tame tangle manifolds are PL manifolds. The canonical PL structures of open or compact tame $m$-tangles restrict to PL $m$-manifold structures on tame tangle manifolds.

Tame tangles approximate transversal tangles. Any compact framed transversal $m$-tangle can be approximated by compact tame $m$-tangles.

Tame tangle presentation conjecture. Every smooth manifold can be presented as a tame tangle.