A Little Microlocal Morse Theory

Details A Little Microlocal Morse Theory A Little Microlocal Morse Theory

2000-06-24

arxiv.org/abs/math/0006185v2

Mathematics

Algebraic Geometry

18 pages

Scientific paper

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.

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