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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 238, Pages 144–157
(Mi tm350)
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This article is cited in 10 scientific papers (total in 10 papers)
Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial
S. M. Gusein-Zadea, F. Delgadob, A. Campillob a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Valladolid
Abstract:
We discuss some results that describe an expression for the Alexander polynomial (and, thus, for the zeta-function of the classical monodromy transformation) of a plane curve singularity in terms of the ring of functions on a curve. They describe the coefficients of the Alexander polynomial as Euler characteristics of some explicitly constructed complements to arrangements of projective hyperplanes in projective spaces. We also discuss the notion of integral with respect to the Euler characteristics over the projectivization of the space of functions (in the spirit of the motivic integration) and its connection with the formulas for the coefficients of the Alexander polynomial.
Received in September 2000
Citation:
S. M. Gusein-Zade, F. Delgado, A. Campillo, “Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial”, Monodromy in problems of algebraic geometry and differential equations, Collected papers, Trudy Mat. Inst. Steklova, 238, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 144–157; Proc. Steklov Inst. Math., 238 (2002), 134–147
Linking options:
https://www.mathnet.ru/eng/tm350 https://www.mathnet.ru/eng/tm/v238/p144
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Abstract page: | 395 | Full-text PDF : | 109 | References: | 58 |
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