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• W2962737777 abstract "We analyze four-dimensional symplectic manifolds of type <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X equals upper S Superscript 1 Baseline times upper M cubed> <mml:semantics> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo>×<!-- × --></mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>X=S^1 times M^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M cubed> <mml:semantics> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>M^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an open <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifold admitting inequivalent fibrations leading to inequivalent symplectic structures on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For the case where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M cubed subset-of upper S cubed> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>M^3 subset S^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the complement of a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=4> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=application/x-tex>4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-component link constructed by McMullen-Taubes, we provide a general algorithm for computing the monodromy of the fibrations explicitly. We use this algorithm to show that certain inequivalent symplectic structures are distinguished by the dimensions of the primitive cohomologies of differential forms on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also calculate the primitive cohomologies on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a class of open <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifolds that are complements of a family of fibered graph links in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S cubed> <mml:semantics> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:annotation encoding=application/x-tex>S^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this case, we show that there exist pairs of symplectic forms on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, arising from either equivalent or inequivalent pairs of fibrations on the link complement, that have different dimensions of the primitive cohomologies." @default.
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• W2962737777 date "2022-10-03" @default.
• W2962737777 modified "2023-10-13" @default.
• W2962737777 title "Symplectic structures with non-isomorphic primitive cohomology on open 4-manifolds" @default.
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• W2962737777 doi "https://doi.org/10.1090/tran/8747" @default.
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