Research seminar "Introduction to the theory of knots"

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

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

Course type:

Compulsory course

When:

2 year, 1, 2 module

Instructor

Gurevich, Elena

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
• контрольная работа

Interim Assessment

• 2024/2025 2nd module
  0.7 * доклад + 0.1 * доклад + 0.2 * контрольная работа

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

• POCHINKA OLGA VITALEVNA
• GUREVICH ELENA Iakovlevna
• NOZDRINOVA ELENA Viacheslavovna