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March 2022 Cohomology of contact loci
Nero Budur, Javier Fernández de Bobadilla, Quy Thuong Lê, Hong Duc Nguyen
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J. Differential Geom. 120(3): 389-409 (March 2022). DOI: 10.4310/jdg/1649953456

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 their tangent cones are homotopy equivalent.

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Nero Budur. Javier Fernández de Bobadilla. Quy Thuong Lê. Hong Duc Nguyen. "Cohomology of contact loci." J. Differential Geom. 120 (3) 389 - 409, March 2022. https://doi.org/10.4310/jdg/1649953456

Information

Received: 4 December 2019; Accepted: 1 September 2020; Published: March 2022
First available in Project Euclid: 15 April 2022

Digital Object Identifier: 10.4310/jdg/1649953456

Rights: Copyright © 2022 Lehigh University

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Vol.120 • No. 3 • March 2022
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