The topology of symplectic manifolds

By Robert E. Gompf. 2001

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View Paper: https://www.semanticscholar.org/paper/9829a7c0a77a6c07c716238a5b8072757b44fd73

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Citations in the corpus

Almost toric symplectic four-manifolds (2003, background): “The importance of Lefschetz fibrations in symplectic topology emerged after Donaldson [9] showed that, after blowing up a sufficient number of points, any closed symplectic four-manifold admits a Lefschetz fibration and Gompf [14] showed how to put a symplectic structure on any four-manifold equippe”
Lagrangian matching invariants for fibred four-manifolds: I (2006, methodology): “Proof For existence, one uses the Thurston‐Gompf method: see [ 14, Theorem 2.2 ] and also [7, Lemma 4.4].”
Lefschetz pencils and divisors in moduli space (2000, background): “The pencil of curves, both before and after the modification by T −1 , has only irreducible fibres and hence does define a canonical symplectic structure by the theorem of Gompf mentioned in the Introduction.”
Toward a topological characterization of symplectic manifolds (2002, methodology): “rphic and hence is (ωY,f)-tame. The ﬁnal hypothesis for Thurston’s construction guarantees the existence of a suitable class c, and the remaining hypotheses of Theorem 3.1 are now easily veriﬁed (cf. [G2]). The family of symplectic forms resulting from Theorem 3.1 is the same one obtained by Thursto”
Lefschetz pencils and the canonical class for symplectic four-manifolds (2000, methodology): “gτ ∂τ . We will use these explicit presentations later to obtain almost-complex structures on Xr(f) with helpful “genericity” properties. For now, we turn to symplectic structures. According to Gompf [Gom], given any map of compact almost-complex manifolds π: (Z;JZ) →(B;JB) for which •Badmits a symp”