V. I. , Index of a singular point of a vector field, the Petrovski-Oleinik inequality, and mixed Hodge structures, Funct. Anal. and its Appli, vol.12, pp.1-14, 1978.

K. Bekka, Regular stratification of subanalytic sets, Bull. London Math. Soc, vol.25, issue.1, pp.7-16, 1993.

J. Bochnak, M. Coste, and M. F. Roy, Géométrie algébrique réelle, vol.12, 1987.

J. W. Bruce, Euler characteristics of real varieties, Bull. London Math. Soc, vol.22, pp.547-552, 1990.

G. Comte and M. Merle, Equisingularité réelle II : invariants locaux et conditions de régularité, Ann. Sci. ´ Ec. Norm. Supér, issue.4, pp.221-269, 2008.

M. Coste and M. Reguiat, Trivialités en famille, Real algebraic geometry, pp.193-204, 1524.

A. Dimca and L. , Real singularities and dihedral representations, Workshop on Real and Complex Singularities, vol.12, pp.67-82, 1996.

A. Durfee, Neighborhoods of algebraic sets, Trans. Amer. Math. Soc, vol.276, issue.2, pp.517-530, 1983.

N. Dutertre, On the topology of semi-algebraic functions on closed semi-algebraic sets, Manuscripta Mathematica, vol.139, issue.3-4, pp.415-441, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00545183

N. Dutertre, Euler characteristic and Lipschitz-Killing curvatures of closed semialgebraic sets, Geom. Dedicata, vol.158, issue.1, pp.167-189, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00453032

N. Dutertre, Stratified critical points on the real Milnor fibre and integral-geometric formulas, Journal of Singularities, vol.13, pp.87-126, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00848992

N. Dutertre, Euler obstruction and Lipschitz-Killing curvatures, Israël Journal of Mathematics, vol.213, pp.109-137, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00995743

N. Dutertre, R. Araújo, and . Santos, Topology of real Milnor fibrations for non-isolated singularities, International Mathematics Research Notices, issue.16, pp.4849-4866, 2016.

D. Eisenbud and H. I. Levine, An algebraic formula for the degree of a C ? map-germ, Annals of Mathematics, vol.106, pp.19-44, 1977.

T. Fukui, An algebraic formula for a topological invariant of bifurcation of 1-parameter family of function-germs, Stratifications, singularities, and differential equations, Travaux en cours, vol.55, pp.45-54, 1990.

G. M. Khimshiashvili, On the local degree of a smooth map, Soobshch. Akad. Nauk Gruz. SSR, vol.85, pp.309-312, 1977.

K. Kurdyka, On gradients of functions definable in o-minimal structures, Ann. Inst. Fourier, vol.48, issue.3, pp.769-784, 1998.

I. N. Iomdin, Complex surfaces with a one-dimensional set of singularities, Sibirsk. Mat. Z, vol.15, pp.1061-1082, 1974.

D. T. Lê, Calcul du nombre de cyclesévanouissantscyclesévanouissants d'une hypersurface complexe, Ann. Inst. Fourier, vol.23, issue.4, pp.261-270, 1973.

D. T. Lê, Ensembles analytiques complexes avec lieu singulier de dimension un (d'après I, Séminaire sur les Singularités, pp.87-95, 1980.

T. L. Loi, Thom stratifications for functions definable in o-minimal structures on, vol.324, pp.1391-1394, 1997.

T. L. Loi, Verdier and strict Thom stratifications in o-minimal structures, Illinois J. Math, vol.42, issue.2, pp.347-356, 1998.

J. Milnor, Singular points of complex hypersurfaces, Ann. Math. Stud, vol.61, 1968.

D. B. Massey, The Lê varieties, I., Invent. Math, vol.99, issue.2, pp.357-376, 1990.

D. B. Massey, The Lê varieties, II., Invent. Math, vol.104, issue.1, pp.113-148, 1991.

D. B. Massey, Lê cycles and hypersurface singularities, Lecture Notes in Mathematics, vol.1615, 1995.

D. B. Massey, Prepolar deformations and a new Lê-Iomdine formula, Pacific J. Math, vol.174, issue.2, pp.459-469, 1996.

D. B. Massey and D. Siersma, Deformation of polar methods, Ann. Inst. Fourier, vol.42, issue.4, pp.737-778, 1992.

X. V. Nguyen, S. Trivedi, and D. Trotman, A geometric proof of the existence of definable Whitney stratifications, Illinois J. Math, vol.58, issue.2, pp.381-389, 2014.

D. Siersma, The monodromy of a series of hypersurface singularities, Comment. Math. Helv, vol.65, issue.2, pp.181-197, 1990.

Z. Szafraniec, On the Euler characteristic of analytic and algebraic sets, Topology, vol.25, issue.4, pp.411-414, 1986.

Z. Szafraniec, Topological invariants of weighted homogeneous polynomial, Glasgow Math. Journal, vol.33, pp.241-245, 1991.

Z. Szafraniec, A formula for the Euler characteristic of a real algebraic manifold, Manuscripta Mathematica, vol.85, pp.345-360, 1994.

B. Teissier, Introduction to equisingularity problems, Proc. Sympos. Pure Math, vol.29, pp.593-632, 1975.

B. Teissier, Variétés polaires. I. Invariants polaires des singularités d'hypersurfaces, Invent. Math, vol.40, issue.3, pp.267-292, 1977.

D. Van-straten and T. Warmt, Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities, Math. Proc. Cambridge Philos. Soc, vol.158, issue.2, pp.249-268, 2015.

C. T. Wall, Topological invariance of the Milnor number mod 2, Topology, vol.22, pp.345-350, 1983.

L. Laboratoire-angevin-de-recherche-en-mathématiques, C. Umr6093, U. Angers, and . Mathstic,