Constructing Lefschetz fibrations via daisy substitutions

Anar Akhmedov, Naoyuki Monden

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We construct new families of nonhyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words (c1c2 ⋯ c2g-1c2gc2g+1 2c2g � c2g-1 ⋯ c2c1)2 = 1, (c1c2 ⋯ c2gc2g+1)2g+2 = 1, and (c1c2 ⋯ c2g-1c2g)2(2g+1) = 1 in themapping class group Γg of the closed orientable surface of genus g, and we study the sections of theseLefschetz fibrations. Furthermore, we show that the total spaces of some of these Lefschetz fibrations are irreducible exotic 4-manifolds, and we compute their Seiberg-Witten invariants. By applying the knot surgery to the family of Lefschetz fibrations obtained from the word (c1c2 ⋯ c2gc2g+1)2g+2 = 1 via daisy substitutions, we also construct an infinite family of pairwise nondiffeomorphic irreducible symplectic and nonsymplectic 4-manifolds homeomorphic to (g2 - g + 1)ℂℙ2#(3g2 - g(k - 3) + 2k +3)ℂℙ2 for any g ≥ 3 and k = 2, ⋯, g + 1.

Original languageEnglish
Pages (from-to)501-529
Number of pages29
JournalKyoto Journal of Mathematics
Volume56
Issue number3
DOIs
Publication statusPublished - Sep 1 2016
Externally publishedYes

Fingerprint

Lefschetz Fibration
Substitution
4-manifold
Seiberg-Witten Invariants
Class Group
Fibration
Homeomorphic
Surgery
Knot
Pairwise
Genus
Closed
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Constructing Lefschetz fibrations via daisy substitutions. / Akhmedov, Anar; Monden, Naoyuki.

In: Kyoto Journal of Mathematics, Vol. 56, No. 3, 01.09.2016, p. 501-529.

Research output: Contribution to journalArticle

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