Pseudo-Anosov dilatations and the Johnson filtration
Justin Malestein, Andrew Putman
TL;DR
This paper establishes explicit lower bounds for the dilatations of pseudo-Anosov mapping classes within the Johnson filtration, addressing a question posed by Farb-Leininger-Margalit.
Contribution
It provides the first explicit bounds for dilatations in the Johnson filtration, linking geometric properties with algebraic filtration levels.
Findings
Explicit lower bounds for dilatations are derived.
The bounds depend on the filtration level k.
The results answer an open question in the field.
Abstract
Answering a question of Farb-Leininger-Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration of the mapping class group.
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