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2017 Positive factorizations of mapping classes
R İnanç Baykur, Naoyuki Monden, Jeremy Van Horn-Morris
Algebr. Geom. Topol. 17(3): 1527-1555 (2017). DOI: 10.2140/agt.2017.17.1527

Abstract

In this article, we study the maximal length of positive Dehn twist factorizations of surface mapping classes. In connection to fundamental questions regarding the uniform topology of symplectic 4–manifolds and Stein fillings of contact 3–manifolds coming from the topology of supporting Lefschetz pencils and open books, we completely determine which boundary multitwists admit arbitrarily long positive Dehn twist factorizations along nonseparating curves, and which mapping class groups contain elements admitting such factorizations. Moreover, for every pair of positive integers g and n, we tell whether or not there exist genus-g Lefschetz pencils with n base points, and if there are, what the maximal Euler characteristic is whenever it is bounded above. We observe that only symplectic 4–manifolds of general type can attain arbitrarily large topology regardless of the genus and the number of base points of Lefschetz pencils on them.

Citation

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R İnanç Baykur. Naoyuki Monden. Jeremy Van Horn-Morris. "Positive factorizations of mapping classes." Algebr. Geom. Topol. 17 (3) 1527 - 1555, 2017. https://doi.org/10.2140/agt.2017.17.1527

Information

Received: 24 September 2015; Revised: 13 May 2016; Accepted: 7 June 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762595
MathSciNet: MR3677934
Digital Object Identifier: 10.2140/agt.2017.17.1527

Subjects:
Primary: 20F65, 53D35, 57R17

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 3 • 2017
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