The vanishing neighbourhood of non-isolated singularities

Details The vanishing neighbourhood of non-isolated singularities The vanishing neighbourhood of non-isolated singularities

2004-11-25

arxiv.org/abs/math/0411572v3

Israel J. Math. 157 (2007), 309--322.

Mathematics

Complex Variables

10 p, 1 fig; more edits

Scientific paper

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of nearby sections. Our standpoint allows to find, in certain cases, the structure of the Milnor fibre up to the homotopy type.

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