TMA4190 Introduction to Topology - Spring 2022
Dear all,
Best of luck with your future studies in topology!
Best wishes,
Marius
Schedule | Room | ||
---|---|---|---|
Lectures: | Monday | 12.15 - 14.00 | S6 |
Tuesday | 08.15 - 10.00 | EL6 | |
Exam: | Oral exams | ||
Marius Thaule | |||
Office: | 1248 Sentralbygg 2 | ||
Email: | marius [dot] thaule [at] ntnu [dot] no |
What this course is about
This course is a first introduction to topology. It will start with basic concepts in point set topology (e.g. topological spaces, continuous maps, metric spaces, constructions of topological spaces, compactness, connectedness). Then it will give an introduction to algebraic topology, such as homotopy, fundamental group, and covering spaces.
See the study handbook for more information.
What you need to know before this course
You should have seen multivariate calculus and linear algebra. Ideally you should have taken TMA4150 Algebra and/or MA3201 Rings and Modules as well, but if you haven't don't worry!
If you have any questions, just contact me!
Lecture Plan
The first lectures will be January 10 and 11.
Lecture | Date | Topic | Notes |
---|---|---|---|
1.1 | 10.01 | Introduction. Continuous maps | Chapter 1 and 2 |
1.2 | 11.01 | Continuous maps. Topological spaces | Chapter 2 and 3 |
2.1 | 17.01 | Topological spaces | Chapter 3 |
2.2 | 18.01 | Topological spaces. Exercises | Chapter 3 |
3.1 | 24.01 | Exercises. Generating topologies | Chapter 2 and 4 |
3.2 | 25.01 | Generating topologies | Chapter 4 |
4.1 | 31.01 | Generating topologies. Exercises | Chapter 3 and 4 |
4.2 | 01.02 | Constructing spaces | Chapter 5 |
5.1 | 07.02 | Constructing spaces | Chapter 5 |
5.2 | 08.02 | Constructing spaces | Chapter 5 |
6.1 | 14.02 | Constructing spaces. Exercises. Topological properties | Chapter 4, 5 and 6 |
6.2 | 15.02 | Topological properties | Chapter 6 |
7.1 | 21.02 | Topological properties | Chapter 6 |
7.2 | 22.02 | Topological properties | Chapter 6 |
8.1 | 28.02 | Topological properties | Chapter 6 |
8.2 | 01.03 | Topological properties. Exercises | Chapter 5 and 6 |
9.1 | 07.03 | Exercises. The fundamental group | Chapter 5 and 7 |
9.2 | 08.03 | The fundamental group | Chapter 7 |
10.1 | 14.03 | The fundamental group | Chapter 7 |
10.2 | 15.03 | The fundamental group | Chapter 7 |
11.1 | 21.03 | The fundamental group. Exercises. The fundamental group of the circle | Chapter 6, 7 and 8 |
11.2 | 22.03 | The fundamental group of the circle | Chapter 8 |
12.1 | 28.03 | The fundamental group of the circle | Chapter 8 |
12.2 | 29.03 | The fundamental group of the circle | Chapter 8 |
13.1 | 04.04 | The fundamental group of the circle | Chapter 8 |
13.2 | 05.04 | Exercises. Summary | Chapter 1 through 7 |
14.1 | 18.04 | Cancelled due to Easter break | |
14.2 | 19.04 | Cancelled due to Easter break | |
15.1 | 25.04 | Summary/Exercises | Chapter 1 through 8 |
15.2 | 26.04 | Exercises | Chapter 8 |
Course material
- Lecture notes
References
We will not follow any particular textbook.
Some interesting books:
- [A] M.A. Armstrong, Basic Topology, Springer-Verlag, 1983.
- [AF] C. Adams and R. Franzosa, Introduction to Topology. Pure and Applied, Pearson Prentice Hall, 2008.
- [Croo] F.H. Croom, Basic Concepts of Algebraic Topology, Springer-Verlag, 1978.
- [Cros] M. Crossley, Essential Topology, Spring-Verlag, 2005.
- [H] A. Hatcher, Algebraic Topology, Cambridge University Press, 2000.
- [J] K. Jänich, Topology, Springer, 1984.
- [Ma] J.P. May, A Concise Course in Algebraic Topology, Chicago Lectures in Mathematics, 1999.
- [Mu] J.R. Munkres, Topology: a first course, Second edition, Prentice-Hall, 2000.
- [S] T.B. Singh, Introduction to Topology, Springer-Verlag, 2019.
Exam
Oral exams.