- Docente: Stefano Francaviglia
- Credits: 6
- SSD: MAT/03
- Language: English
- Moduli: Stefano Francaviglia (Modulo 1) Alessia Cattabriga (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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
Lectures with modality depending on pandemic protocols.
Assessment methods
Oral examination
Teaching tools
Text books, .pdf files and/or recording of online lectures.
Office hours
See the website of Stefano Francaviglia
See the website of Alessia Cattabriga