One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists

Abstract

We obtain a presentation of a certain orientation preserving periodic homeomorphism of a compact real surface of genus $g\ge 2$ by a product of right handed Dehn twists using a splitting family. It was expected that a presentation of a homeomorphism by right handed Dehn twists obtained from a splitting family is one of the shortest presentation. In this paper, we give a counter example of this conjecture.