Introduction to Algebraic Topology

4 Credits.

This course introduces the central ideas and tools of algebraic topology, with an emphasis on exposure rather than technical depth. Students will learn how algebraic structures such as chain complexes, homology, and cohomology can be used to study and distinguish topological spaces. Key topics include simplicial complexes, the Snake Lemma, the Universal Coefficient Theorem, and the Künneth Theorem, with a focus on concrete examples and computations.The course also explores broader frameworks such as the Eilenberg–Steenrod axioms and CW complexes, along with cellular (co)homology. Time permitting, students will encounter spectral sequences and their applications. By the end of the course, students will have a working familiarity with the main concepts and techniques of algebraic topology, preparing them for further study in topology and related fields.