Algebraic Topology I Autumn 2024
- Lecturer
- Paul Biran
- Coordinator
- Giovanni Ambrosioni
General informations and contents
- Content. This is an introductory course in algebraic topology, which is the study of algebraic invariants of topological spaces. The main topics we will cover are singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. We will assume a basic knowledge of point-set topology and group theory.
We encourage students to familiarise with the concepts of covering space and fundamental group (as treated for instance in Hatcher's or Bredon's books in the literature).
- Lectures. Lectures will take place on Wednesdays between 10.15 and 12.00 and Fridays between 14.15 and 16.00 in HG E 1.1.
Recordings of all the lectures will be provided at the following link.
- Exercise classes and Forum. In this course we won't have weekly exercise sessions, but some lectures during the semester will be replaced by exercise sessions led by the course organiser. Apart from this, there is the possibility of asking questions on the DMATH forum:
there you will find a post dedicated to each exercise sheet, where you can ask (and answer!) questions related to exercises, but don't hesitate to create a 'new topic' if you have any other math-related question. Suggestions for topics to discuss during the exercise classes are very welcome!
- Old notes and recordings. You can find recordings and handwritten notes of a past edition of the lecture at this link.
Old exams
Exercises
Exercise sheets and their solutions will be posted here. We will roughly have one exercise sheet a month. Note that exercise sheets will not be graded, but if you have questions feel free to use the dedicated post on the forum or directly email the organiser.
Literature
-
G. Bredon, "Topology and geometry", Graduate Texts in Mathematics, 139. Springer-Verlag, 1997.
(Through the ETH Zurich network members of ETH can legally download this and other ebooks.)
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A. Hatcher, "Algebraic topology", Cambridge University Press, Cambridge, 2002.
See also:
A. Hatcher.
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E. Spanier, "Algebraic topology", Springer-Verlag