Vanishing cycles and singularities of meromorphic functions
نویسندگان
چکیده
We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs – as initiated by Milnor in the sixties – and of the global topology of polynomial functions, which has been advanced more recently. We define singularities along the poles with respect to a certain (weak) stratification and prove local and global bouquet structure in case of isolated singularities. In general, splitting of vanishing homology at singular points and global Picard-Lefschetz phenomena occur. key words: vanishing cycles, singularities along the poles, topology of meromorphic functions
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2 Arnaud Bodin and Mihai Tibăr
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