Journal of the Mathematical Society of Japan

Positive factorizations of symmetric mapping classes

Tetsuya ITO and Keiko KAWAMURO

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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.

Article information

J. Math. Soc. Japan, Volume 71, Number 1 (2019), 309-327.

Received: 13 September 2017
First available in Project Euclid: 20 November 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57M07: Topological methods in group theory

symmetric mapping class positive factorization quasipositive braid


ITO, Tetsuya; KAWAMURO, Keiko. Positive factorizations of symmetric mapping classes. J. Math. Soc. Japan 71 (2019), no. 1, 309--327. doi:10.2969/jmsj/78827882.

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