Generalized symplectic rational blowdowns

By Margaret Symington. 2001

70 citations recorded by the source corpus.

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category. AMS Classication 57R17; 57R15, 57M50

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2049083959938c5a854a52373e934c3e68809234

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Four dimensions from two in symplectic topology (2002, background): “. Completing this to a ﬁbration over (B,A,S) as in the proof of Theorem 5.2 we are not guaranteed of getting a unique Lagrangian ﬁbration (see San [33]). However the proof of Proposition 4.8 given in [36] shows that the structure of the ﬁbration can be perturbed via a compactly supported symplectic ”
Rational blowdowns and smoothings of surface singularities (2006, methodology): “It has been shown by Symington [31, 32] that a configuration Γp/q of symplectic spheres in a symplectic 4-manifold can be blown down symplectically; that is, the symplectic form, when restricted to the complement of the spheres, extends to the rational homology disk.”
A simply connected surface of general type with pg=0 and K2=2 (2006, background): “fold containing a conﬁguration Cp,q such that all 2-spheres ui in Cp,q are symplectically embedded and intersect positively, then the rational blow-down manifold Mp also admits a symplectic structure [22, 23]. Now we perform a rational blow-down surgery of the surface Z obtained in the main construc”
An exotic smooth structure on CP^2+6CP^2-bar (2004, background): “Since our operation is a special case of the generalized rational blow-down process, which is proved to be symplectic when performed along symplectically embedded spheres [19], we conclude:”
Symplectic theory of completely integrable Hamiltonian systems (2011, background): “That is what Symington does in [99] to show that neighborhoods of focus-focus fibers are always symplectomorphic (after forgetting the foliation, of course).”
Almost toric symplectic four-manifolds (2003, background): “The proof of this proposition given in [38] can easily be modified to accommodate multiple singularities on the nodal fiber.”