On Heegaard diagrams (Q1364803)

Let \(h\) be a homeomorphism of a handlebody \(H\) to itself. If the restriction of \(h\) to the boundary \(\partial H\) of \(H\) is a product of Dehn twists along a system of pairwise disjoint curves in \(H\), then it is shown that every one of the curves must bound a disc in \(H\). In particular, \(h\) itself is then a product of Dehn twists along discs. This result is proved by showing that every marking of a closed surface can be transformed, using Hatcher-Thurston moves alone, into a waveless position with respect to any fixed marking.