Journal of the Mathematical Society of Japan

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

Mizuho ISHIZAKA

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 1 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1149166790

Digital Object Identifier
doi:10.2969/jmsj/1149166790

Mathematical Reviews number (MathSciNet)
MR2228574

Zentralblatt MATH identifier
1100.14005

Subjects
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

Keywords
monodromy algebraic curves mapping class group

Citation

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. https://projecteuclid.org/euclid.jmsj/1149166790


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References

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