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...
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Elementary Mathematics (K-6) Explained: / playlist
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Ancient Mathematics: • Ancient Mathematics
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Sociology and Pure Mathematics: • Sociology and Pure Mat...
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Math History: • MathHistory: A course ...
Wild Trig: Intro to Rational Trigonometry: • WildTrig: Intro to Rat...
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Boole's Logic and Circuit Analysis: • Boole's Logic and Circ...
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Differential Geometry: • Differential Geometry
Algebraic Topology: • Algebraic Topology
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[@kabayakawa]

Algebraic topology is now my favorite topic. Thanks for so good material

[@njwildberger]

If two loops are homotopic, they define the same class in the fundamental group. The inverses of the two loops will also by homotopic. So the inverses are well defined in the fundamental group.

[@njwildberger]

@vivaelche05 Sorry, I will only be teaching this again in our second semester, which starts in August. I will be adding more videos to the series probably in Sept or Oct.
Sorry for the delay.

[@njwildberger]

@yexonlau Possibly. I will be adding some more lectures later this year.

[@Maturandin91]

Thanks so much!!! You can explain better than all assistants and profs I've ever had. ;-)

[@henf5671]

Another wonderful video. You explain this so clearly! Thanks again for posting these videos.

[@hoangyuotube]

Thank prof njwildberger a lot. It's wonderful.

[@davidcooper4327]

Thanks for the response, I think I got it now. I'm thoroughly enjoying the lectures.

[@Relative0]

Thanks Professor! Very very much appreciated. Watching your video's are like a mathematicians version of a big budget Hollywood movie!

[@njwildberger]

@8223765 I will be adding some homology theory to these lectures later in the year.

[@hellenakinyi7942]

Video Content
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...

[@njwildberger]

@vivaelche05 It will appear in about half a year!

[@8223765]

Thanks for this video. Very interesting and easy to understand. I would also be interested in the van Kampen theorem. And maybe some homology theorie too.

[@pragnabhatt3703]

THANK YOU!!!

[@vivaelche05]

@njwildberger Thanks for your reply. Professor Wildberger, would it at all be possible for you to post the lecture videos one by one before 6 months?

[@dibeos]

How do I put 10 likes?!