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Topological invariants of weighted homogeneous polynomials

Published online by Cambridge University Press:  18 May 2009

Zbigniew Szafraniec
Affiliation:
Institute of Mathematics, University of Gdańsk, 80–952 Gdańsk, Wita Stwosza 57, Poland
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Let ℝn → ℝ be a weighted homogeneous polynomial such that df(0) = 0, L = {xSn−1|f(x) = 0}, and let χ(L) be the Euler characteristic of L. The problem is how to calculate χ(L) in terms of f.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Arnold, V. I., Index of a singular point of a vector field, the Petrovski-Oleinik inequality, and mixed hodge structures, Functional Anal. Appl. 2 (1978), 111.CrossRefGoogle Scholar
2.Eisenbud, D. and Levine, H. I., An algebraic formula for the degree of a C°° map germ, Ann. of Math. (2) 7 (1977), 1944.CrossRefGoogle Scholar
3.Hardt, R., Semi-algebraic local triviality in semi-algebraic mappings, Amer. J. Math. 102 (1980), 291302.CrossRefGoogle Scholar
4.Lojasiewicz, S., Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 449474.Google Scholar
5.Milnor, J., Singular points of complex hypersurfaces (Princeton University Press, 1968).Google Scholar
6.Szafraniec, Z., On the Euler characteristic of analytic and algebraic sets, Topology 25 (1986), 411414.CrossRefGoogle Scholar
7.Szafraniec, Z., On the Euler characteristic of complex algebraic varieties, Math. Ann. 280 (1988), 177183.CrossRefGoogle Scholar
8.Szafraniec, Z., On the Euler characteristic mod 2 of real projective varieties, Math. Proc. Cambridge Philos. Soc. 104 (1988), 479481.CrossRefGoogle Scholar
9.Wall, C. T. C., Topological invariance of the Milnor number mod 2, Topology 22 (1983), 345350.CrossRefGoogle Scholar