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Families of functions dominated by distributions of C -classes of mappings

Goo Ishikawa — 1983

Annales de l'institut Fourier

A subsheaf of the sheaf ℰ Ω of germs C ∞ functions over an open subset Ω of R n is called a sheaf of sub C ∞ function. Comparing with the investigations of sheaves of ideals of ℰ Ω , we study the finite presentability of certain sheaves of sub C ∞ -rings. Especially we treat the sheaf defined by the distribution of Mather’s 𝒞 -classes of a C ∞ mapping.

Symplectic classification of parametric complex plane curves

Goo Ishikawa;  Stanisław Janeczko — 2010

Annales Polonici Mathematici

Based on the discovery that the δ-invariant is the symplectic codimension of a parametric plane curve singularity, we classify the simple and uni-modal singularities of parametric plane curves under symplectic equivalence. A new symplectic deformation theory of curve singularities is established, and the corresponding cyclic symplectic moduli spaces are reconstructed as canonical ambient spaces for the diffeomorphism moduli spaces which are no longer Hausdorff spaces.

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