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Orientation-preserving self-homeomorphisms
of the surface of genus two
have points of period at most two


Authors: Warren Dicks and Jaume Llibre
Journal: Proc. Amer. Math. Soc. 124 (1996), 1583-1591
MSC (1991): Primary 55M20; Secondary 57M20, 54H20, 57M60
MathSciNet review: 1301020
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Abstract: We show that for any orientation-preserving self-homeomorphism $\alpha $ of the double torus $\Sigma _{2}$ there exists a point $p$ of $\Sigma _{2}$ such that $\alpha (\alpha (p)) = p$. This answers a question raised by Jakob Nielsen in 1942.


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Additional Information

Warren Dicks
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona,08193 Bellaterra (Barcelona), Spain
Email: dicks@mat.uab.es

Jaume Llibre
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona,08193 Bellaterra (Barcelona), Spain
Email: imat0@cc.uab.es

DOI: https://doi.org/10.1090/S0002-9939-96-03131-0
Received by editor(s): September 22, 1994
Communicated by: Mary Rees
Article copyright: © Copyright 1996 American Mathematical Society