68 research outputs found
Interpolation of characteristic classes of singular hypersurfaces
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a
nonsingular variety M `interpolates' between two other notions of
characteristic classes for singular varieties, provided that the singular locus
of X is smooth and that certain numerical invariants of X are constant along
this locus. This allows us to define a lift of the Chern-Schwartz-MacPherson
class of such `nice' hypersurfaces to intersection homology. As another
application, the interpolation result leads to an explicit formula for the
Chern-Schwartz-MacPherson class of X in terms of its polar classes.Comment: 10 page
Formes de Whitney et primitives relatives de formes diff\'erentielles sous-analytiques
Let be a real-analytic manifold and a proper
triangulable subanalytic map. Given a subanalytic -form on
whose pull-back to every non singular fiber of is exact, we show tha
has a relative primitive: there is a subanalytic -form
such that . The proof uses a subanalytic
triangulation to translate the problem in terms of "relative Whitney forms"
associated to prisms. Using the combinatorics of Whitney forms, we show that
the result ultimately follows from the subanaliticity of solutions of a special
linear partial differential equation. The work was inspired by a question of
Fran\c{c}ois Treves
O Teorema de Poincare-Hopf
The Poincare-Hopf Theorem is one of the most used in other areas of science.
There are applications of the Poincare-Hopf Theorem in physics, chemistry,
biology and even in economics, psychology, etc ... The Poincare-Hopf Theorem
connects an invariant of combinatorial, the character of Euler-Poincare to an
invariant of differential geometry, index of vector fields. The results that
connect two very different areas of mathematics can be considered as the most
beautiful, useful and fruitful.Comment: in Portugues
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