5 problems

Fix a smooth knot type $K$. A transverse representative $T$ of $K$ has a standard neighborhood, whose boundary has a slope, and standard neighborhoods are considered up to contact…

Let $T$ be a transverse knot in a contact manifold. A standard neighborhood of $T$ has a boundary slope, measured with respect to the chosen framing, and standard neighborhoods are…

Negative stabilization nonuniqueness conjecture. Negative stabilization is not a unique operation on virtual transverse knots. That is, there are two ways to negatively stabilize s…

Transverse-to-virtual injectivity conjecture. No two transverse knots are the same virtual transverse knot.

Let $K$ be a fibered knot in $S^3$. The UTP conjecture. $K$ fails the uniform thickness property if and only if $xi_K \cong xi_{std}$, and hence if and only if $K$ is fibered stron…