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The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities

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Abstract

In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of the Bruce-Roberts number in terms of differential forms and the Lê-Greuel formula.

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Acknowledgements

This research has been supported by the Research Foundation of São Paulo (FAPESP), Grand no: 2017/23555-9.

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  1. ICMC-USP, Av. Trabalhador Sancarlsense, 400, São Carlos, Sào Paulo, Brazil

    Konstantinos Kourliouros

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  1. Konstantinos Kourliouros
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Correspondence to Konstantinos Kourliouros.

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Kourliouros, K. The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities. Bull Braz Math Soc, New Series 52, 405–413 (2021). https://doi.org/10.1007/s00574-020-00209-6

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  • DOI: https://doi.org/10.1007/s00574-020-00209-6

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