Hurwitz equivalence for lefschetz fibrations and their multisections

R. Inanç Baykur, Kenta Hayano

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

In this article, we characterize isomorphism classes of Lefschetz fibrations with multisections via their monodromy factorizations. We prove that two Lefschetz fibrations with multisections are isomorphic if and only if their monodromy factorizations in the relevant mapping class groups are related to each other by a finite collection of modifications, which extend the well-known Hurwitz equivalence. This in particular characterizes isomorphism classes of Lefschetz pencils. We then show that, from simple relations in the mapping class groups, one can derive new (and old) examples of Lefschetz fibrations which cannot be written as fiber sums of blown-up pencils.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages1-24
Number of pages24
DOIs
Publication statusPublished - 2016

Publication series

NameContemporary Mathematics
Volume675
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Hurwitz equivalence
  • Lefschetz fibration
  • Mapping class group
  • Multisectin
  • Positive factorization

ASJC Scopus subject areas

  • Mathematics(all)

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