On the geography of symplectic 6-manifolds

Halic, Mihai

doi:10.1007/s002290050179

Cited by 12 publications

(22 citation statements)

References 3 publications

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“…Next, we state a proposition which will be useful in the fundamental group computations of our examples obtained via the symplectic connected sum operation. The proof of this proposition can be found in [20] and [23]. Proposition 3.3.…”

Section: Symplectic Connected Summentioning

confidence: 92%

On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature

Akhmedov

Sakallı

2016

Topology and its Applications

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ABSTRACT. In [7,4], the first author and his collaborators constructed the irreducible symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n − 1)CP 2 #(2n − 1)CP 2 for each integer n ≥ 25, and the families of simply connected irreducible nonspin symplectic 4-manifolds with positive signature that are interesting with respect to the symplectic geography problem. In this paper, we improve the main results in [7,4]. In particular, we construct (i) an infinitely many irreducible symplectic and non-symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n − 1)CP 2 #(2n − 1)CP 2 for each integer n ≥ 12, and (ii) the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signature and with more than one smooth structure. Our construction uses the complex surfaces of Hirzebruch and Bauer-Catanese on BogomolovMiyaoka-Yau line with c 2 1 = 9χ h = 45, along with the exotic symplectic 4-manifolds constructed in [2,5,3,6,10].

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Section: Symplectic Connected Summentioning

confidence: 92%

On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature

Akhmedov

Sakallı

2016

Topology and its Applications

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“…These tori are Lagrangian, but we can perturb the symplectic form so that one of them, say T = µ × a becomes symplectic. Moreover, π 1 (X \ T ) = 1, which follows from the Van Kampen's Theorem using the facts that π 1 (X) = 1 and the rim torus has a dual sphere (see Proposition 1.2 in [20], or Gompf [17], page 564). Hence, we have a symplectic torus T in X of self-intersection 0 such that π 1 (X \ T ) = 1.…”

Section: Construction Of Exotic 4-manifolds Via Lantern Substitutionmentioning

confidence: 94%

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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“…Now we construct 8-dimensional manifolds by using symplectic 4-manifolds given by Gompf [5] and Halic [6].…”

Section: Symplectic 8-manifolds With Spin(7) -Structurementioning

confidence: 99%

“…Let (N6 , ω N , Ω N ) be a Calabi-Yau 3-fold where ω N is the Kähler (symplectic) 2-form and Ω N is a holomorphic volume form. When M 8 = N × R 2 , then the holonomy group Hol(M ) ⊆ SU(3) ⊂ Spin(7) .…”

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confidence: 99%