3 citations · 11 across the 11 of their papers we have counts for
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math.AG2010
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…
math.GT2010
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.
math.AG2010
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