The fundamental group of the circle

This is the second video for the course Topologie en Meetkunde taught in Utrecht University. We introduce the fundamental group, and we compute it in the case of the real line and the circle. Once you watch the video, try to answer the following question: How would you endow the fundamental group with its group structure? (Attempt first to see what is going on in the case of the circle!). https://www.seevid.ir/fa/w/CFtXsm5-JmE Recap https://www.seevid.ir/fa/w/CFtXsm5-JmE Statement of the results https://www.seevid.ir/fa/w/CFtXsm5-JmE The real line https://www.seevid.ir/fa/w/CFtXsm5-JmE Euclidean space is contractible https://www.seevid.ir/fa/w/CFtXsm5-JmE Loops in the circle https://www.seevid.ir/fa/w/CFtXsm5-JmE The real line covers the circle https://www.seevid.ir/fa/w/CFtXsm5-JmE Lifting paths https://www.seevid.ir/fa/w/CFtXsm5-JmE Homotopies https://www.seevid.ir/fa/w/CFtXsm5-JmE Summary Website of the Utrecht Geometry Centre: http://utrechtgeometrycentre.nl/ Lecturer: Álvaro del Pino (https://alvarodelpino.com/)

• #education
• #mathematics
• #algebraic_topology
• #loops
• #paths
• #homotopies
• #fundamental_group