AlgTop25: More on the fundamental group

A continuation on the fundamental group of a surface, we prove that the multiplication of equivalence classes or types of loops from a base point does indeed form a group in the algebraic sense. We discuss the fundamental group of the torus and the projective plane.

This is part of a beginner's course on Algebraic Topology, given by N J Wildberger of UNSW.
Video Contents:
00:00 More on the fundamental group
01:50 Multiplication
03:04 Theorem
03:50 Proof -Identity & constant loop
08:40 Inverses
16:00 Associativity
20:00 picture examples
30:06 Projective plane
33:56 Problem 26. Describe...

************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/...

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  

Here are the Wild Egg Maths Playlists (some available only to Members!)

   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
************************