Deformations of functions on surfaces

Abstract

The paper contains a review on recent progress in the deformational properties of smooth maps from compact surfaces $M$ to a one-dimensional manifold $P$. It covers description of homotopy types of stabilizers and orbits of a large class of smooth functions on surfaces obtained by the author, E. Kudryavtseva, B. Feshchenko, I. Kuznietsova, Yu. Soroka, A. Kravchenko. We also present here a new direct proof of the fact that for generic Morse maps the connected components their orbits are homotopy equivalent to finite products of circles.

41 page

References in corpus (2)

• Orbits of smooth functions on 2-torus and their homotopy types
• Smooth functions on 2-torus whose Kronrod-Reeb graph contains a cycle