TL;DR
This paper develops a method to compute the number of stratified Morse singularities in linear Morsifications of functions with arbitrary singular loci, linking these counts to topological invariants.
Contribution
It introduces a way to effectively compute stratified Morse singularities for functions with complex singular loci, extending classical results beyond isolated singularities.
Findings
Effective computation of stratified Morse singularities
Connection between Morse counts and topological invariants
Extension of Milnor fibre topology analysis
Abstract
The number of Morse points in a Morsification determines the topology of the Milnor fibre of a holomorphic function germ with isolated singularity. If 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 .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology