This course is an introduction to albraic topology and is designed for PA mathematics students, as well as PA MAP and INFO students who are interested in DataScience or in theorical informatics, and who wish to acquire a strong mathematics education. This course is a good preparation (without being a prerequisite) and complement to IN556 course (Topological Data Analysis), the introduced tools current applications to scatter plot study.
The course will focus on study of invariants in topological spaces, particularly homology. After some review on topology and the study of homotopy equivalence notion, we introduce and singular homology and their main properties. The fundamental group will also be introduced. The end of the course will focus on general ideas of homologic algebra offering different applications from the main part of the course to the study of other mathematics objects. During the course, ideas and notions of category theory will be introduced and used.
Bibliography
Glenn Bredon, Topology and Geometry, Graduate Texts in Mathematics, 139. Springer-Verlag, New York,
1997
Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002
Chuck Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38.
Cambridge University Press, Cambridge, 1994
Course language: French
- Teaching coordinator: Deroin Bertrand
- Teaching coordinator: Ginot Grégory