論文

査読有り
2017年

Positive factorizations of mapping classes

ALGEBRAIC AND GEOMETRIC TOPOLOGY
  • R. Inanc Baykur
  • ,
  • Naoyuki Monden
  • ,
  • Jeremy Van Horn-Morris

17
3
開始ページ
1527
終了ページ
1555
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.2140/agt.2017.17.1527
出版者・発行元
GEOMETRY & TOPOLOGY PUBLICATIONS

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.

リンク情報
DOI
https://doi.org/10.2140/agt.2017.17.1527
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000409988300006&DestApp=WOS_CPL
ID情報
  • DOI : 10.2140/agt.2017.17.1527
  • ISSN : 1472-2739
  • Web of Science ID : WOS:000409988300006

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