Topics in Topology 2022
This is the homepage for the Master's course Topics in Topology at RuG. The goal of this course is to study three and four-dimensional manifolds using some diagrammatic instructions, called Kirby calculus. For the latter, the study of knots becomes essential.
Lectures: Monday 11-13 & Thursday 13-15 in NB 5115.0014 (16).
Shared overleaf document with the lecture notes (to be written by you!). See the course description below.
In this seminar course, participants are expected to give two 30-minute talks about a topic of their choice among the marked with (SP) in the schedule. They must also elaborate a detailed, self-contained handout about their talk, to be brought along to the meeting. Students are also required to prepare some exercises to have a joint discussion after their talk. Attendance to every meeting is required. We urge participants to stick to 30 minutes during their talks (for that some good advice is to rehearse the talk and time oneself).
Students will also be assigned to type one of the Monday lectures in this shared overleaf document, to create some joint lecture notes at the end of the course. Everyone is welcome (and strongly encouraged) to check the other's typing and correct mistakes or add extra information.
There will also be two homework sets throughout the course.
Students should be familiar with basic concepts of topological spaces, differential geometry and commutative algebra. Knowledge from the courses Introduction to metric and topological spaces, linear algebra, group theory, multivariable analysis and analysis on manifolds will suffice.
The final grade will be based on your presentation (50%), practical work (25%) and homework and lecture notes (25%).
Our two main references will be of
[GS] Gompf, Stipsicz, 4-Manifolds and Kirby calculus (chapters 4 and 5)
[Sa] Saveliev, N. - Lectures on the topology of 3-manifolds
Other references that will become handy:
[Ha] Hatcher, A. - Algebraic Topology
[KS] Kirby, R. & Scharlemann, M. - Eight faces of the Poincaré homology 3-sphere
[Li] Lickorish, R. - An introduction to knot theory
[Ro] Rolfsen, D. - Knots and links.