Research seminar "Introduction to the theory of knots"

2023/2024

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:

Курс обязательный

Когда читается:

2-й курс, 1, 2 модуль

Преподаватель

Гуревич Елена Яковлевна

Course Syllabus

Abstract

The discipline is taught in the second year of the master's degree. It is aimed at an introduction to the theory of knots.

Learning Objectives

• The aim of the course is to introduce the notion of a knot and its properties, as well as to dive into some important aspects of homotopy theory with the help of this notion.

Expected Learning Outcomes

• solve typical problems and able to explain the solution

Course Contents

• Inavriants of knots and links in S^3
• Knots in R^4
• Knots in dynamics

Assessment Elements

• доклад
• In-class assignment

Interim Assessment

• 2023/2024 2nd module
  0.2 * In-class assignment + 0.4 * доклад + 0.4 * доклад

Bibliography

Recommended Core Bibliography

• A combinatorial introduction to topology, Henle, M., 1994
• Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
• The geometry and physics of knots, Atiyah, M., 2004
• Topology, Munkres, J. R., 2000

Recommended Additional Bibliography

• Differential topology, Hirsch, M. W., 1976