TY - JOUR
T1 - Constructing Lefschetz fibrations via daisy substitutions
AU - Akhmedov, Anar
AU - Monden, Naoyuki
N1 - Publisher Copyright:
© 2016 by Kyoto University.
PY - 2016/9
Y1 - 2016/9
N2 - 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.
AB - 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.
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U2 - 10.1215/21562261-3600148
DO - 10.1215/21562261-3600148
M3 - Article
AN - SCOPUS:84983551876
SN - 0023-608X
VL - 56
SP - 501
EP - 529
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 3
ER -