96778 - Knot Theory and Applications

Learning outcomes

At the end of the course, the student knows the basics of knot theory and some applications. In particular the student knows the relation between links and braids and is able to compute numerical, polynomial and algebraic invariants. The student is aware of how this theory could be used in biochemical models and is able to solve problems in this setting.

Course contents

Knot and link in the space and in S3. Equivalence of knots, difference between isotopy and ambient isotopy. Representation of knots via planar diagrams. Knot invariants (colorability, polynomial invariants, etc...). Knot complements, fundamental group and other invariants. Applications.

Readings/Bibliography

K. Murasugi "Knot theory and its applications"

A. Kawauchi "A survey of knot theory"

R. Lickorish "An Introduction to knot theory"

D. Rolfsen "Knots and Links"

Teaching methods

Traditional lectures in presence.

Assessment methods

Oral exam with a presentation on a research paper.

Teaching tools

Notes of the course.

Office hours

See the website of Alessia Cattabriga

See the website of Stefano Francaviglia