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September 2016 Constructing Lefschetz fibrations via daisy substitutions
Anar Akhmedov, Naoyuki Monden
Kyoto J. Math. 56(3): 501-529 (September 2016). DOI: 10.1215/21562261-3600148

Abstract

We construct new families of nonhyperelliptic Lefschetz fibrations by applying the daisy substitutions to the families of words ( c 1 c 2 c 2 g 1 c 2 g c 2 g + 1 2 c 2 g c 2 g 1 c 2 c 1 ) 2 = 1 , ( c 1 c 2 c 2 g c 2 g + 1 ) 2 g + 2 = 1 , and ( c 1 c 2 c 2 g 1 c 2 g ) 2 ( 2 g + 1 ) = 1 in the mapping class group Γ g of the closed orientable surface of genus g , and we study the sections of these Lefschetz 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 ( c 1 c 2 c 2 g c 2 g + 1 ) 2 g + 2 = 1 via daisy substitutions, we also construct an infinite family of pairwise nondiffeomorphic irreducible symplectic and nonsymplectic 4 -manifolds homeomorphic to ( g 2 g + 1 ) CP 2 # ( 3 g 2 g ( k 3 ) + 2 k + 3 ) CP ¯ 2 for any g 3 and k = 2 , , g + 1 .

Citation

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Anar Akhmedov. Naoyuki Monden. "Constructing Lefschetz fibrations via daisy substitutions." Kyoto J. Math. 56 (3) 501 - 529, September 2016. https://doi.org/10.1215/21562261-3600148

Information

Received: 1 July 2014; Revised: 9 March 2015; Accepted: 13 May 2015; Published: September 2016
First available in Project Euclid: 22 August 2016

zbMATH: 1351.57032
MathSciNet: MR3542772
Digital Object Identifier: 10.1215/21562261-3600148

Subjects:
Primary: 57R55
Secondary: 57R17

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 3 • September 2016
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