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There are several things going on here, explained rather elliptically in the paper. Let me expand. First, there's the question of which holomorphic annuli double-cover the disk. More precisely, suppos …

To expand on Lee's answer, recall that Teichmüller space can be divided up into a "thin part" (where some geodesic is short, or equivalently where some conformal annulus has large modulus), and its co …

For the first question, the answer is yes. Geometrization implies that the only non-Haken manifolds irreducible manifolds are compact hyperbolic manifolds (with no cusps), and there again $\pi_1$ is …

The Bennequin bound [1] says that, for a transverse knot (or later link) $K$ in $S^3$, $$\mathrm{sl}(K) \le - \chi(\Sigma)$$ for any Seifert surface $\Sigma$ for $K$, where $\mathrm{sl}$ is the self-l …

If the orginal link $U_1 \cup U_2$ was hyperbolic, the answer is yes. For large enough $n$, $S^3 \setminus K(n)$ will also be hyperbolic, and will approach $S^3 \setminus (U_1 \cup U_2)$ in the Grom …

First off, the mapping class group of a surface with boundary is generally taken to mean the group of diffeomorphisms that fix the boundary, up to isotopies fixing the boundary. In this context, a De …