Kodaira dimension of fiber sums along spheres

Dorfmeister, Josef G.

doi:10.1007/s10711-014-9974-2

Cited by 12 publications

(9 citation statements)

References 28 publications

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“…We will also need the following lemmas, which are due to R. Gompf, to analyze the symplectic 4-manifolds constructed in Section 6. For the proof we refer the reader to [18] and [8]. See also the work of J. Dorfmeister [7,8] who gives a related criteria on symplectic minimality and how the symplectic Kodaira dimension changes under the rational blowdown along a symplectic −4 sphere (see also related work in [9]).…”

Section: Rational Blowdown and Lantern Relationsmentioning

confidence: 99%

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Akhmedov

Park

2014

Mathematical Research Letters

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Motivated by the construction of H. Endo and Y. Gurtas, changing a positive relator in Dehn twist generators of the mapping class group by using lantern substitutions, we show that 4-manifold K3#2CP 2 equipped with the genus two Lefschetz fibration can be rationally blown down along six disjoint copies of the configuration C 2 . We compute the Seiberg-Witten invariants of the resulting symplectic 4-manifold, and show that it is symplectically minimal. Using our example, we also construct an infinite family of pairwise non-diffeomorphic irreducible symplectic and non-symplectic 4-manifolds homeomorphic to M = 3CP 2 #(19 − k)CP 2 for 1 ≤ k ≤ 4.

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Section: Rational Blowdown and Lantern Relationsmentioning

confidence: 99%

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Akhmedov

Park

2014

Mathematical Research Letters

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“…For the latter class, by a change of basis, they are the class F − 2S in S 2 × S 2 #(k − 1)CP 2 which clearly has a symplectic representative (here F and S denotes the fiber and base homology classes in S 2 × S 2 ). Therefore, the following lemma implies Theorem 1.8: 10 has an ω-symplectic representative for some ω with K ω = K st .…”

Section: 21mentioning

confidence: 79%

Stability and existence of surfaces in symplectic 4-manifolds with b ⁺=1

Dorfmeister

2016

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Abstract. We establish various stability results for symplectic surfaces in symplectic 4−manifolds with b + = 1. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify negative symplectic spheres in symplectic 4−manifolds with κ = −∞. This involves the explicit construction of spheres in rational manifolds via a new construction technique called the tilted transport.

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“…We will also need the following lemmas, which are due to R. Gompf, to analyze the symplectic 4-manifolds constructed in Section 3. For the proof we refer the reader to [18,11]. Lemma 15.…”

Section: 5mentioning

confidence: 99%

Unique fiber sum decomposability of genus 2 Lefschetz fibrations

Park

2017

Topology and its Applications

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Abstract. By applying the lantern relation substitutions to the positive relation of the genus two Lefschetz fibration over S 2 . We show that K3#2CP 2 can be rationally blown down along seven disjoint copies of the configuration C 2 . We compute the Seiberg-Witten invariant of the resulting symplectic 4-manifolds, and show that they are symplectically minimal. We also investigate how these exotic smooth 4-manifolds constructed via lantern relation substitution method are fiber sum decomposable. Furthermore by considering all the possible decompositions for each of our decomposable exotic examples, we will find out that there is a uniquely decomposing genus 2 Lefschetz fibration which is not a self sum of the same fibration up to diffeomorphism on the indecomposable summands.

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Kodaira dimension of fiber sums along spheres

Cited by 12 publications

References 28 publications

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Stability and existence of surfaces in symplectic 4-manifolds with b ⁺=1

Unique fiber sum decomposability of genus 2 Lefschetz fibrations

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Kodaira dimension of fiber sums along spheres

Cited by 12 publications

References 28 publications

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Lantern substitution and new symplectic 4-manifolds with $b_2{}^{+} = 3$

Stability and existence of surfaces in symplectic 4-manifolds with b +=1

Unique fiber sum decomposability of genus 2 Lefschetz fibrations

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Stability and existence of surfaces in symplectic 4-manifolds with b ⁺=1