We study a question of Etnyre and Van Horn-Morris whether a symmetric mapping class admitting a positive factorization is a lift of a quasipositive braid. We answer the question affirmatively for mapping classes satisfying certain cyclic conditions.
The first author was partially supported by JSPS KAKENHI Grant number 15K17540 and 16H02145. The second author was partially supported by NSF grant DMS-1206770 and Simons Foundation Collaboration Grants for Mathematicians 426710.
"Positive factorizations of symmetric mapping classes." J. Math. Soc. Japan 71 (1) 309 - 327, January, 2019. https://doi.org/10.2969/jmsj/78827882