Topological equivalence of smooth functions with isolated critical points on a closed surfaces
Abstract
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re$z^k$ for the some nonnegative integer k. The full topological invariant of such functions is constructed.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 1999
- DOI:
- 10.48550/arXiv.math/9912004
- arXiv:
- arXiv:math/9912004
- Bibcode:
- 1999math.....12004P
- Keywords:
-
- Mathematics - Geometric Topology;
- 57R45;
- 57R70;
- 58C27
- E-Print:
- 12 pages without figures