# Kunakovskaya O.V. Boundary topological indices of a pair of vector fields and existence theorems (abstract)

Speaker: Olga Kunakovskaya

Title: Boundary topological indices of a pair of vector fields and existence theorems

Abstract:
The problem of the existence of solutions of equations of the type

${\displaystyle F_{2}(x)=\lambda F_{1}(x)}$

will be discussed. The method of topological boundary index is proposed. The topological boundary (bi)index ${\displaystyle B(F_{1},F_{2})}$ is additive and admits also a local form. The construction for smooth fields ${\displaystyle F_{1},F_{2}}$ and some applications one can find in the monograph: Kunakovskaya O.V. Topological indices of a pair of fields (Topologicheskije indexi pary polej). Voronezh, Nauchnaya kniga, 2020. 88 pp., in Russian.

Video
Slides: KunakovskayaAMVconf2021slides.pdf

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.