Signature bounds and plumbing constructions for divides
Livio Liechti · arXiv (Cornell University) · 2014
Abstract. We give the optimal lower bound for the signature of any slalom divide knot in terms of its genus. This yields a lower bound for the topological four-ball genus of slalom divide knots. We also show that the signature of any nontrivial divide knot is strictly positive and that in this general case, there exists no better bound for the signature in terms of genus. Furthermore, the question whether the fiber surfaces of divide knots are plumbings of trefoil fibers is considered. 1.