Lecturer: Dr. José Pedro Quintanilha
Links: Müsli, heiCO
Lectures: Monday 09:15 - 10:45 in SR 3

This lecture is classified as a "Spezialisierungsmodul".

There are no exercise classes, but if you wish to participate in the course, please register on Müsli for the dummy tutorial.

Evaluation

Evaluation is through an oral examination at the end of the semester.

To take the exam, students need to register on heiCO for both the lecture and the exercise class, and to contact me for scheduling the exam.

Program

Pre-requisites: algebraic topology (fundamental groups, coverings, singular (co)homology), basic differential topology (smooth manifolds, orientations)

  1. Introduction: knots, links, link isotopy, equivalent characterizations, link diagrams, Reidemeister's Theorem.
    Notes.
  2. Colorability of knots: p-colorings of a diagram, the Fox p-coloring space, invariance, computations, twist knots.
  3. Seifert Surfaces: oriented knots and links, Seifert's algorithm, the knot genus.
  4. The connected sum of knots: connected sum of manifold pairs, construction of the knot connected sum, properties of the connected sum, additivity of genus, prime knots, the prime decomposition theorem.

Literature

All material will be contained in the lecture notes, but here are some additional resources: