A {note on the generalized} M{atsumoto relation}

Dalyan, Elif; Medetogullari, E.; Pamuk, Mehmetcik

doi:10.3906/mat-1512-87

Cited by 3 publications

(4 citation statements)

References 3 publications

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“…. , 8, we obtain genus-2 Lefschetz fibrations of the types (12,9), (14,8), (16,7), (18,6), (20,5), (22,4), (24,3), (26,2). They are all minimal by Proposition 6, and once we show that X i is simply-connected, we can once use Theorem 13 again to conclude that X i is an exotic 3CP 2 #(11 + i)CP 2 , for i = 1, .…”

Section: Exotic Symplectic Rational Surfacesmentioning

confidence: 99%

“…Lastly, for n + 2s = 30, the pairs (2,14), (4,13), (6,12) are ruled out by the second inequality in Lemma 5, and (28, 1), (30, 0) by (22).…”

Section: Lemma 12mentioning

confidence: 99%

“…We are thus left with the possible values (8,6), (10,5), (12,4) when b + = 1 and (10, 10), (12,9), (14,8), (16, 7), (18,6), (20,5), (22,4), (24,3), (26,2) when b + = 3. In all these cases s > 0, so the presence of a reducible fiber implies that there exists a homology class with an odd intersection number.…”

Section: Lemma 12mentioning

confidence: 99%

“…For n + 2s = 20, the pairs (2, 9), (4,8) are eliminated using the second inequality in Lemma 5,and (14,3), (16,2), (18,1), (20,0) by (22).…”

Section: Lemma 12mentioning

confidence: 99%

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Small Lefschetz fibrations and exotic 4-manifolds

Baykur

Korkmaz

2016

Math. Ann.

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Abstract. We explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces CP 2 #p CP 2 for p = 7, 8, 9, and to 3CP 2 #q CP 2 for q = 12, . . . , 19. Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with b + ≤ 3, with one possible exception when b + = 3. Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of CP 2 #4CP 2 and 3CP 2 #6CP 2 from small Lefschetz fibrations over surfaces of higher genera.

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