...with affection and respect, for all the pleasure of working with Xavier INDEX OF SINGULARITIES OF REAL VECTOR FIELDS ON SINGULAR HYPERSURFACES
نویسندگان
چکیده
Gómez-Mont, Seade and Verjovsky introduced an index, now called GSV-index, generalizing the Poincaré-Hopf index to complex vector fields tangent to singular hypersurfaces. The GSV-index extends to the real case. This is a survey paper on the joint research with Gómez-Mont and Giraldo about calculating the GSV-index IndV±,0(X) of a real vector field X tangent to a singular hypersurface V = f(0). The index IndV±,0(X) is calculated as a combination of several terms. Each term is given as a signature of some bilinear form on a local algebra associated to f and X . Main ingredients in the proof are Gómez-Mont’s formula for calculating the GSV-index on singular complex hypersurfaces and the formula of Eisenbud, Levine and Khimshiashvili for calculating the Poincaré-Hopf index of a singularity of a real vector field in R.
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