Regular homotopy of Hurwitz curves
Abstract
We prove that any two irreducible cuspidal Hurwitz curves C0 and C1 (or more generally, curves with A-type singularities) in the Hirzebruch surface FN with coinciding homology classes and sets of singularities are regular homotopic; and symplectically regular homotopic if C0 and C1 are symplectic with respect to a compatible symplectic form.
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