The fundamental group | Algebraic Topology | NJ Wildberger

This lecture introduces the fundamental group of a surface. We begin by discussing when two paths on a surface are homotopic, then defining multiplication of paths, and then multiplication of equivalence classes or types of loops based at a fixed point of the surface.

The fundamental groups of the disk and circle are described.

This is part of a beginner's course on Algebraic Topology given by N J Wildberger at UNSW.

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[doublecheeseburgirl-]

topologists always look so joyful when theyre talking about the subject i love it

[sambaoabol]

Now I understand part of algebraic topology. Thanks

[njwildberger]

There is a big difference. General topological spaces are fraught with logical difficulties, but surfaces are more concrete and closer to what we can effectively specify computationally. Moreover we have a nice understanding of two dimensional surfaces; in higher dimensions it is much more murky.

[njwildberger]

It's not impossible to describe that fundamental group. We are still just talking about closed loops, now in three dimensional space, up to homotopy--in this case avoiding two particular lines.

[matematicale]

Thank you for sharing this, Professor! I wish more of your collegues from all around the world did it!

[yeast]

Great lecture, made very easy to understand

[ilmLilkul]

thank you thank you thank you!! this is helping me so much... and its nice to see that your sticking with your opinion on the use of infinity when you could have just called it an equivalence class and got on with the lesson.

[maynardtrendle]

Thanks for everything you do Mr.Wildberger!

[naynay]

Thanks for posting I was beginning to hate Algebraic Topology but you've explained it really well!

[rewtnode]

If you have in a group a different left inverse and right inverse, so you can’t write for the inverse Y of X : X * Y = Y * X = e, then is that still a group?

[dkwc]

thanks for your video, I am the beginner for this subject, under fundamental group, are all the homotopic paths necessary to keep constant total time or keep constant total length keep or keep constant velocity. because velocity*Time = path length, which variables is necessary to keep constant for all homotopic paths under fundamental group ????

[yingqishi]

This is so awesome! Thanks Sir very much

[clapacademyarmandnoel]

Why wasn't closure listed as a group property? That, along with the three listed, establishes the full definition of a group.