3 citations · 11 across the 11 of their papers we have counts for
15 papers
Equi-singularity of real families and Lipschitz Killing curvature densities at infinity
Nicolas Dutertre, Vincent Grandjean
Fix an o-minimal structure expanding the ordered field of real numbers. Let be a definable family of closed subsets of whose total space $…
Principal Kinematic Formulas for Germs of Closed Definable Sets
Nicolas Dutertre
We prove two principal kinematic formulas for germs of closed definable sets in , that generalize the Cauchy-Crofton formula for the density due to Comte and the infi…
Gauss-Kronecker Curvature and equisingularity at infinity of definable families
Nicolas Dutertre, Vincent Grandjean
Assume given a polynomially bounded o-minimal structure expanding the real numbers. Let be a globally definable one parameter family of -hypersurface…
On the topology of non-isolated real singularities
Nicolas Dutertre
Khimshiashvili proved a topological degree formula for the Eu-ler characteristic of the Milnor fibres of a real function-germ with an isolated singularity. We give two generalizati…
Global Euler obstruction, global Brasselet numbers and critical points
Nicolas Dutertre, Nivaldo G. Grulha
Let be an equidimensional complex algebraic set and let be a polynomial function. For each , we define the global Brassel…
Lipschitz-Killing curvatures and polar images
Nicolas Dutertre
We relate the Lipschitz-Killing measures of a definable set in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of $\…
Fibrations structure and degree formulae for Milnor fibers
Nicolas Dutertre, Raimundo N. Araújo Dos Santos, Ying Chen +1
In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We gi…
Euler obstruction and Lipschitz-Killing curvatures
Nicolas Dutertre
Applying a local Gauss-Bonnet formula for closed subanalytic sets to the complex analytic case, we obtain characterizations of the Euler obstruction of a complex analytic germ in t…
Stratified critical points one the real Milnor fibre and integral-geometric formulas
Nicolas Dutertre
Let be the germ of a closed subanalytic set and let and be two subanalytic functions. Under some conditi…
Topology of real Milnor fibration for non-isolated singularities
Nicolas Dutertre, Raimundo N. Araújo Dos Santos
We consider a real analytic map , , that satisfies Milnor's conditions (a) and (b) introduced by D…
Lê-Greuel type formula for the Euler obstruction and applications
Nicolas Dutertre, Nivaldo G. Grulha
The Euler obstruction of a function can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a…
On the topology of semi-algebraic functions on closed semi-algebraic sets
Nicolas Dutertre
We consider a semi-algebraic function defined on a closed semi-algebraic set X. We give formulas relating the topology of X to the indices of the critical points of the function an…
On the topology of stable maps
Nicolas Dutertre, Toshizumi Fukui
We investigate how Viro's integral calculus applies for the study of the topology of stable maps. We also discuss several applications to Morin maps and complex maps.
Euler characteristic and Lipschitz-Killing curvatures of closed semi-algebraic sets
Nicolas Dutertre
We prove a formula that relates the Euler-Poincaré characteristic of a closed semi-algebraic set to its Lipschitz-Killing curvatures
Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets
Nicolas Dutertre
The radial index of a 1-form on a singular set is a generalization of the classical Poincaré-Hopf index. We consider different classes of closed semi-analytic sets in R^n that cont…