Introduction to symplectic topology
Citations
1,412 citations
Cites background from "Introduction to symplectic topology..."
...[McS1], so we again focus on the main applications to 4-manifold topology while avoiding unnecessary coverage of other aspects of these theories....
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...While many useful examples come from algebraic geometry [BPV] and symplectic topology [McS1], perhaps the most powerful general technique for existence results (particularly for manifolds with small Betti numbers) is Kirby calculus....
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1,380 citations
1,275 citations
Cites methods from "Introduction to symplectic topology..."
...For example, Moser’s method applied to symplectic forms ω (see for example [ 15 ]) shows that the cohomology class [ω] ∈ H2(M,R) is a local modulus up to diffeomorphism for symplectic manifolds and clearly the cohomology class of the B-field in H2(M,R) defines B up to exact...
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641 citations
Additional excerpts
...ential form ρ= eB+iωΩ, where Ω is decomposable of degree 0 ≤ k≤ nand such that ωn−k ∧ Ω∧ Ω 6= 0 . Weinstein’s proof of the Darboux normal coordinate theorem for a family of symplectic structures (see [33]) can be used to find a leaf-preserving local diffeomorphism ϕtaking ωto a 2-form whose pullback to each leaf is the standard Darboux symplectic form on R 2n− k, i.e. ϕ∗ω R2n−2k×{pt} = ω 0 = dx 1 ∧ dx 2...
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575 citations