Narrow Results

We give a visual construction of stable maps from the $3$-sphere into the real plane enjoying the following properties: the set of definite fold points coincides with a given two-bridge link and the map only admits restricted types of fibers containing two indefinite fold points. As a corollary, we determine the stable map complexities defined by Ishikawa and Koda for sufficiently complicated two-bridge link exteriors.

We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine the canonical component of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.

We consider some families of links which include $(-2,2m+1,2n)$-pretzel links and twisted Whitehead links. We calculate the ${\mathrm{\text{SL}}}_2(ℂ)$-character varieties of these families, and determine the number of irreducible components of these character varieties.

In his previous work, the author proved that the canonical decompositions of hyperbolic fibered two-bridge link complements are layered. This implies that they admit taut structures. In this paper, we completely determine, for each hyperbolic fibered two-bridge link, whether the canonical decomposition of its complement is veering with respect to the taut structure.