Poincaré-Hopfs theorem on singular varieties

Resumen:

The classical Poincaré-Hopf theorem establishes a deep connection between the total index of a vector field on a smooth closed manifold, and the topology of the manifold in question. In these lectures we will discuss extensions of this theorem to the case of singular varieties. This is related to the basic question of defining what the local index of a vector field is when we consider vector fields on singular varieties.

This course will be planned in concondance with the course of Jean-Paul Brasselet.

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