Eighth problem of the Arnold trivium
Geometric Topology
2024-03-15 v1 Mathematical Physics
math.MP
Abstract
We give a full and detailed solution of eighth Arnold's trivium problem. We find critical points of a smooth function on a given one-parametric two-dimensional surface with Lagrange multipliers method. Basic Morse theory and Poincare-Hopf theorem makes it possible to determine a genus of this surface and gives a beautiful training example of Morse surgery on a two-dimensional surface of genus .
Keywords
Cite
@article{arxiv.2403.08803,
title = {Eighth problem of the Arnold trivium},
author = {Timur Kenzhaev},
journal= {arXiv preprint arXiv:2403.08803},
year = {2024}
}