Journal of the Mathematical Society of Japan

Positive factorizations of symmetric mapping classes

Tetsuya ITO and Keiko KAWAMURO

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Abstract

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.

Note

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1542704619

Digital Object Identifier
doi:10.2969/jmsj/78827882

Mathematical Reviews number (MathSciNet)
MR3909923

Zentralblatt MATH identifier
07056566

Subjects
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

Keywords
symmetric mapping class positive factorization quasipositive braid

Citation

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. https://projecteuclid.org/euclid.jmsj/1542704619


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