6 problems

Let ${\cal K}$ be a topological knot type, and let a minimum-braid-index representative of ${\cal K}$ admit a negative flype. A transversally simple knot type is one for which the…

A template is a branched $2$-manifold with a semiflow, and a braid presentation of a template is a presentation in which its periodic orbits are represented as braids. Same-crossin…

Let $\lambda$ be a booklink in an open book 3-manifold representing a split link. A split booklink is a booklink admitting a splitting sphere intersecting each component of the bin…

Let $D$ and $D'$ be link-equivalent scannable algebraic divides of the same minimal index. Let $\beta(D)$ and $\beta(D')$ be their associated positive braids; two positive braids a…

Decoration conjecture. The set of horseshoe braid types is partitioned into families $\mathcal D^w=\{\beta^w_q\}$, each parameterized by a rational number $q$, which are totally or…

Exchange-vanishing conjecture. The polynomials ${\bf Q}_{\widehat\beta,1}(x)$ of exchange-related braids vanish in the same way as the Fiedler polynomial; in particular, the first-…