Geodesic
Thom Polynomials for Maps of Curves with Isolated Singularities
Informatics and Automation, Analysis and singularities. Part 1, Tome 258 (2007), pp. 93-106.

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

Thom (residual) polynomials in characteristic classes are used in the analysis of the geometry of function spaces. They serve as a tool for describing the classes that are Poincaré dual to subvarieties of functions with singularities of prescribed types. We give explicit universal expressions for residual polynomials in spaces of functions on complex curves that have isolated singularities and multisingularities, in terms of few characteristic classes. These expressions lead to a partial description of a stratification of Hurwitz spaces. 
@article{TRSPY_2007_258_a8,
     author = {M. E. Kazarian and S. K. Lando},
     title = {Thom {Polynomials} for {Maps} of {Curves} with {Isolated} {Singularities}},
     journal = {Informatics and Automation},
     pages = {93--106},
     publisher = {mathdoc},
     volume = {258},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a8/}
}
TY  - JOUR
AU  - M. E. Kazarian
AU  - S. K. Lando
TI  - Thom Polynomials for Maps of Curves with Isolated Singularities
JO  - Informatics and Automation
PY  - 2007
SP  - 93
EP  - 106
VL  - 258
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a8/
LA  - ru
ID  - TRSPY_2007_258_a8
ER  - 
%0 Journal Article
%A M. E. Kazarian
%A S. K. Lando
%T Thom Polynomials for Maps of Curves with Isolated Singularities
%J Informatics and Automation
%D 2007
%P 93-106
%V 258
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a8/
%G ru
%F TRSPY_2007_258_a8
M. E. Kazarian; S. K. Lando. Thom Polynomials for Maps of Curves with Isolated Singularities. Informatics and Automation, Analysis and singularities. Part 1, Tome 258 (2007), pp. 93-106. http://geodesic.mathdoc.fr/item/TRSPY_2007_258_a8/

[1] Arnold V.I., “Topologicheskaya klassifikatsiya kompleksnykh trigonometricheskikh mnogochlenov i kombinatorika grafov s odinakovym chislom vershin i reber”, Funkts. analiz i ego pril., 30:1 (1996), 1–17 | MR | Zbl

[2] Arnold V.I., “Kriticheskie tochki funktsii i klassifikatsiya kaustik”, UMN, 29:3 (1974), 243–244

[3] Goulden I.P., Jackson D.M., Vakil R., “Towards the geometry of double Hurwitz numbers”, Adv. Math., 198:1 (2005), 43–92 | DOI | MR | Zbl

[4] Kazaryan M.E., “Multiosobennosti, kobordizmy i ischislitelnaya geometriya”, UMN, 58:4 (2003), 29–88 | MR | Zbl

[5] Kazaryan M.E., Morin maps and their characteristic classes, , 2006 http://www.mi.ras.ru/~kazarian/papers/morin.pdf | Zbl

[6] Kazaryan M.E., Lando S.K., “K teorii peresechenii na prostranstvakh Gurvitsa”, Izv. RAN. Ser. mat., 68:5 (2004), 91–122 | MR

[7] Lando S.K., Zvonkin A.K., Graphs on surfaces and their applications, Springer, Berlin, 2004 | MR | Zbl

[8] Zvonkin D., Lando S.K., “O kratnostyakh otobrazheniya Lyashko–Loiengi na stratakh diskriminanta”, Funkts. analiz i ego pril., 33:3 (1999), 21–34 | MR | Zbl

[9] Lando S., Zvonkine D., “Counting ramified coverings and intersection theory on spaces of rational functions. I: Cohomology of Hurwitz spaces”, Moscow Math. J., 7:1 (2007), 85–107 | MR | Zbl

[10] Looijenga E., “The complement of the bifurcation variety of a simple singularity”, Invent. Math., 23 (1974), 105–116 | DOI | MR | Zbl

[11] Okounkov A., “Toda equations for Hurwitz numbers”, Math. Res. Lett., 7:4 (2000), 447–453 | MR | Zbl

[12] Rimányi R., “Multiple point formulas – a new point of view”, Pacif. J. Math., 202:2 (2002), 475–490 | DOI | MR | Zbl

[13] Thom R., “Quelques propriétés globales des variétés différentiables”, Comment. Math. Helv., 28 (1954), 17–86 | DOI | MR | Zbl

[14] Zvonkine D., “Multiplicities of the Lyashko–Looijenga map on its strata”, C. R. Acad. Sci. Paris Sér. 1 yr 1997, 324:12, 1349–1353 | MR | Zbl

[15] Zvonkine D., “Counting ramified coverings and intersection theory on Hurwitz spaces. II: Local structure of Hurwitz spaces and combinatorial results”, Moscow Math. J., 7:1 (2007), 135–162 | MR | Zbl