Local linear Morsifications

Abstract

The number of Morse points in a Morsification determines the topology of the Milnor fibre of a holomorphic function germ f with isolated singularity. If f has an arbitrary singular locus, then this nice relation to the Milnor fibre disappears. We show that despite this loss, the numbers of stratified Morse singularities of a general linear Morsification are effectively computable in terms of topological invariants of f.

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