Explicit special covers of alternating links
arXiv:1909.12266
Abstract
Given a prime, alternating link diagram, we build a special cover of the link complement whose degree is bounded by a factorial function of the crossing number. It follows that a subgroup of the link group of that index embeds into right-angled Artin and Coxeter groups. Corollaries of this result include a quantification of residual finiteness, control of the growth of Betti numbers in covers, and an explicit bound on the rank of a Z-module on which the link group acts faithfully.
Version 1 of the paper contains a basepoint error in Theorem 6.18. In the commutative diagram mentioned in the theorem-statement, the graph of spaces in the top row is not a cover of the graph of spaces in the bottom row, because the basepoints do not join up correctly. Unfortunately, this error invalidates the proof of the main theorem