The course “Basic Topology of Manifolds” is intended for undergraduate students and it lasts in the period: October 20, 2020 — January 26, 2021, with a two week Christmas and the New Year break.

We meet weekly on Mondays and Wednesdays, 17:00–18:30 CET (Central European Time), using the Teams application. Please write to kpa@amu.edu.pl if you wish to attend the course.

The course is designated for students with some familiarity of notions and results used in point set topology, algebra, and analysis.

Basic Topology of Manifolds

Week 01: Manifolds: a gentle introduction
Week 02: Curves and surfaces
Week 03: Manifolds of dimension 3
Week 04: Manifolds of dimension 4
Week 05: Knots and links
Week 06: Braids and links
Week 07: Homotopy groups of manifolds
Week 08: Homology groups of manifolds
Week 09: Classification of manifolds of dimension 2
Week 10: Geometric structures on manifolds of dimension 2
Week 11: Smooth structures on manifolds
Week 12: Smooth vector fields on manifolds
Week 13: Real, complex, and quaternion projective spaces
Week 14: Stiefel manifolds and Grassmann manifolds
Week 15: Compact manifolds with fixed point property