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math.GT2025
On the number of components of folds of image simple fold maps
O. Saeki, R. Sadykov
A smooth map between manifolds is said to be \emph{image simple} if its restriction to its singular point set is a topological embedding. We study the parity of the number of conne…
math.GT2025
On the Mather stability theorem for smooth maps
Rustam Sadykov
In [MaII] Mather proved that a smooth proper infinitesimally stable map is stable. This result is the key component of the Mather stability theorem [MaV], which can be reformulated…
math.GT2025
A homotopy invariant of stable maps to oriented surfaces
Liam Kahmeyer, Rustam Sadykov
The singular set of a generic map of a manifold of dimension to an oriented surface is a closed smooth curve . We study the parity of the number…