Geodesic
Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Monodromy in problems of algebraic geometry and differential equations, Tome 238 (2002), pp. 144-157

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2002_238_a8,
     author = {S. M. Gusein-Zade and F. Delgado and A. Campillo},
     title = {Integrals with {Respect} to the {Euler} {Characteristic} over {Spaces} of {Functions} and the {Alexander} {Polynomial}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {144--157},
     publisher = {mathdoc},
     volume = {238},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_238_a8/}
}
TY  - JOUR
AU  - S. M. Gusein-Zade
AU  - F. Delgado
AU  - A. Campillo
TI  - Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 144
EP  - 157
VL  - 238
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2002_238_a8/
LA  - ru
ID  - TM_2002_238_a8
ER  - 
%0 Journal Article
%A S. M. Gusein-Zade
%A F. Delgado
%A A. Campillo
%T Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 144-157
%V 238
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2002_238_a8/
%G ru
%F TM_2002_238_a8
S. M. Gusein-Zade; F. Delgado; A. Campillo. Integrals with Respect to the Euler Characteristic over Spaces of Functions and the Alexander Polynomial. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Monodromy in problems of algebraic geometry and differential equations, Tome 238 (2002), pp. 144-157. http://geodesic.mathdoc.fr/item/TM_2002_238_a8/