Pseudo–Anosov mapping classes from pure mapping classes
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Abstract:
We study types of mapping classes which arise as a product of a given mapping class and powers of certain pure mapping classes. We derive an explicit constant depending only on a surface such that almost all above pure mapping classes give rise to pseudo–Anosov type whenever their powers are larger than the constant. Throughout this study, we also give various ways of constructing pseudo–Anosov mapping classes. Furthermore, we are able to capture the stable lengths of all pseudo–Anosov mapping classes constructed by our methods.References
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Additional Information
- Yohsuke Watanabe
- Affiliation: University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822
- MR Author ID: 1153472
- Email: ytm.watanabe@gmail.com
- Received by editor(s): September 24, 2018
- Received by editor(s) in revised form: May 29, 2019
- Published electronically: September 6, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 419-434
- MSC (2010): Primary 57M60
- DOI: https://doi.org/10.1090/tran/7919
- MathSciNet review: 4042880