- Docente: Alessia Cattabriga
- Credits: 6
- SSD: MAT/03
- Language: English
- Moduli: Alessia Cattabriga (Modulo 1) Stefano Francaviglia (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Feb 21, 2024 to May 30, 2024
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
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.