Introduction to Knot Theory

2026/2027

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

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 dynamics
• Knots in R^4

Assessment Elements

• Доклад
• Экзамен

Interim Assessment

• 2026/2027 1st module
  1 * Доклад
• 2026/2027 2nd module
  0.5 * Экзамен + 0.5 * 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

Authors

• Bagaev Andrei Vladimirovich
• SARAEV ILIA ALEKSANDROVICH