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The fundamental group | Algebraic Topology | NJ Wildberger

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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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Опубликовано:

1 авг 2024

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Комментарии : 20

@sambaoabol4739 Год назад

Now I understand part of algebraic topology. Thanks

@doublecheeseburgirl- 8 месяцев назад

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

@yeast4529 5 месяцев назад

Great lecture, made very easy to understand

@matematicale 6 лет назад

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

@njwildberger 10 лет назад

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.

@maynardtrendle820 3 года назад

Thanks for everything you do Mr.Wildberger!

@3ilmLilkul 11 лет назад

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.

@njwildberger 10 лет назад

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.

@naynay2703 11 лет назад

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

@yingqishi4627 6 лет назад

This is so awesome! Thanks Sir very much

@baovoquoc6358 8 лет назад

Thanks Sir very much.

@kfqfguoqf 5 лет назад

Thank you!

@bandarmohammeddalreshidi9692 4 года назад

Thank you so much

@ReeshaEducation 3 года назад

Thank you so much sir

@smailpl1043 3 года назад

Nice explaining

@rewtnode 6 лет назад

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?

@dkwc4019 3 года назад

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 ????