Journal of the Mathematical Society of Japan

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


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We obtain a presentation of a certain orientation preserving periodic homeomorphism of a compact real surface of genus g 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.

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J. Math. Soc. Japan, Volume 58, Number 2 (2006), 585-594.

First available in Project Euclid: 1 June 2006

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Zentralblatt MATH identifier

Primary: 14D06: Fibrations, degenerations
Secondary: 14H45: Special curves and curves of low genus 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 57M99: None of the above, but in this section 30F99: None of the above, but in this section

monodromy algebraic curves mapping class group


ISHIZAKA, Mizuho. One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists. J. Math. Soc. Japan 58 (2006), no. 2, 585--594. doi:10.2969/jmsj/1149166790.

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