Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Analysis

Code

aldims1u0um17em

Title

Low dimensional topology (l)

Usual semester

Autumn

Published semester

2025/26/2

ECTS

3

Language

en

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyze mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

handle decompositions of manifolds knots in 3-manifolds, Alexander polynomial the Jones polynomial, applications surfaces and mapping class groups 3-manifolds, examples Heegaard decomposition and Heegaard diagram 4-manifolds, the theorems of Freedman and Donaldson (statement only) Lefschetz fibrations invariants (Seiberg–Witten and Heegaard Floer invariants)

Assessment method

(written or oral) exam plus term mark

Bibliography

lecture notes

Recommended bibliography

J. Milnor: Morse theory. Princeton, 1973. R.E. Gompf, A.I. Stipsicz: 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, Volume 20, Amer. Math. Society. Providence, Rhode Island.

Programmes of the course