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arXiv · 1911.08213

Cohomology of contact loci

Nero Budur·Javier Fernández de Bobadilla·Quy Thuong Lê·Hong Duc Nguyen
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Abstract

We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean's spectral sequence converging to the Floer cohomology of the m-th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs of holomorphic functions are embedded topologically equivalent, then the Milnor fibers of the their tangent cones are homotopy equivalent.

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Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê, Hong Duc Nguyen. 2019-11-19. Cohomology of contact loci. https://arxiv.org/abs/1911.08213

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