Factoring periodic maps into Dehn twists

Factoring periodic maps into Dehn twists

Let Mod(Sg) be the mapping class group of the closed orientable surface Sg of genus g≥1. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop methods for factoring certain roots of Dehn twists as words in Dehn...

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Veröffentlicht in:Journal of pure and applied algebra 2023-01, Vol.227 (1), p.107159, Article 107159
Hauptverfasser: Dhanwani, Neeraj K., Nair, Ajay K., Rajeevsarathy, Kashyap
Format: Artikel
Sprache:eng
Schlagworte:
Dehn twists
Mapping class
Periodic maps
Surface
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Zusammenfassung:Let Mod(Sg) be the mapping class group of the closed orientable surface Sg of genus g≥1. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop methods for factoring certain roots of Dehn twists as words in Dehn twists. We will also show the existence of conjugates of periodic maps of order 4g and 4g+2, for g≥2, whose product is pseudo-Anosov.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2022.107159