1. Introduction and Contents

Algebraic topology studies topological spaces by associating algebraic objects, such as groups, vector spaces, and graded commutative algebras, to them in a functorial way. This introductory course provides the foundations of algebraic topology that are essential for modern geometry, including low-dimensional topology, differential geometry, and algebraic geometry. Topics include the fundamental group, homology, cohomology, characteristic classes, and basic homological algebra.

2. Prerequisites

Undergraduate-level algebra and analysis, together with point-set topology (at the level of https://ppt.cc/f62E6x). Students who have not previously taken courses in complex analysis and geometry are expected to take them concurrently.

3. Grading Scheme

TBA

4. Reference material (textbooks)

TBA

5. Course Credit: 3

Course No.: NCTS5065

Course ID: V41 U2090