Abstract.
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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Received: 15 September 2000 / Published online: 18 June 2001
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Massey, D. A little microlocal Morse theory. Math Ann 321, 275–294 (2001). https://doi.org/10.1007/s002080100227
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DOI: https://doi.org/10.1007/s002080100227