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Research seminar "Introduction to the theory of knots"

2023/2024
Учебный год
ENG
Обучение ведется на английском языке
6
Кредиты

Преподаватель

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

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

Expected Learning Outcomes

  • solve typical problems and able to explain the solution
Course Contents

Course Contents

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

Assessment Elements

  • non-blocking доклад
  • non-blocking In-class assignment
Interim Assessment

Interim Assessment

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

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

  • GUREVICH ELENA Iakovlevna
  • POCHINKA OLGA VITALEVNA