Singular Lefschetz pencils

  title={Singular Lefschetz pencils},
  author={Denis Auroux and Simon K Donaldson and Ludmil Katzarkov},
We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4-manifold equipped with a “near-symplectic” structure (i.e., a closed 2-form which is symplectic outside a union of circles where it vanishes transversely). Our main result asserts that, up to blowups, every near-symplectic 4-manifold (X,ω) can be decomposed into (a) two symplectic Lefschetz fibrations over discs, and (b) a fibre bundle over S1 which relates the boundaries of the Lefschetz fibrations to… CONTINUE READING
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