Title: Fundamental Groups and Covering Spaces
Speaker: Andrey Lazarev
Affiliation: Lancaster University, UK
Location: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
This course introduces the definition and fundamental properties of homotopy groups in algebraic topology, with special emphasis on the first homotopy group (the fundamental group). We will discuss the construction of universal coverings and develop the theory of covering spaces, culminating in their complete classification. The course includes concrete computational examples to illustrate these concepts.
Schedule:
June 25, 2025 (10:00-11:00):
Review of homotopy groups and examples; commutativity of higher homotopy groups.
June 26, 2025 (9:00-10:00):
Covering spaces and their relationship with the fundamental group of the base space.
June 27, 2025 (9:00-10:00):
Computation of fundamental groups via universal coverings. Examples: wedges of circles, tori, Klein bottles, and real projective spaces.
June 28, 2025 (9:00-10:00):
Classification of covering spaces.
Speaker's Biography:
Andrey Lazarev is a Professor at Lancaster University, specializing in algebraic topology and homotopy theory. He previously served as the Editor-in-Chief of the Bulletin of the London Mathematical Society and has published extensively in prestigious journals, including Advances in Mathematics, Proceedings of the London Mathematical Society, and Journal of Noncommutative Geometry. His work bridges abstract theory with computational methods in topology.
