On the Class of Stable Isotopic Connectivity of Gradient-Like Diffeomorphisms of a Two-Dimensional Torus

Student: Dobroliubova Alisa

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2024

In this paper we consider the class of $G$ gradient-like diffeomorphisms of a 2-torus inducing an isomorphism of the fundamental group defined by the matrix $\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}$. The main result of this paper is the following theorem. \begin{theorem}\label{ter}. For any diffeomorphisms of class $G$ there exists a stable arc connecting them. \end{theorem}

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses