A little microlocal Morse theory
Copyright policy )A little microlocal Morse theory
If a complex analytic function, $f$, has a stratified isolated critical point, then it is known that the cohomology of the Milnor fibre of $f$ has a direct sum decomposition in terms of the normal Morse data to the strata. We use microlocal Morse theory to obtain the same result under the weakened hypothesis that the vanishing cycles along $f$ have isolated support. We also investigate an index-theoretic proof of this fact.
18 pages
Analytic sheaves and cohomology groups, Germs of analytic sets, local parametrization, Local complex singularities, Analytic subsets of affine space, Topology of analytic spaces, 32B15, complex analytic functions, Mathematics - Algebraic Geometry, FOS: Mathematics, microlocal Morse theory, Algebraic Geometry (math.AG)
Analytic sheaves and cohomology groups, Germs of analytic sets, local parametrization, Local complex singularities, Analytic subsets of affine space, Topology of analytic spaces, 32B15, complex analytic functions, Mathematics - Algebraic Geometry, FOS: Mathematics, microlocal Morse theory, Algebraic Geometry (math.AG)
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