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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Pseudo-Anosov mapping classes from pure mapping classes


Author: Yohsuke Watanabe
Journal: Trans. Amer. Math. Soc. 373 (2020), 419-434
MSC (2010): Primary 57M60
DOI: https://doi.org/10.1090/tran/7919
Published electronically: September 6, 2019
MathSciNet review: 4042880
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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.


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Additional Information

Yohsuke Watanabe
Affiliation: University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822
Email: ytm.watanabe@gmail.com

DOI: https://doi.org/10.1090/tran/7919
Received by editor(s): September 24, 2018
Received by editor(s) in revised form: May 29, 2019
Published electronically: September 6, 2019
Article copyright: © Copyright 2019 American Mathematical Society