Algebraic Topology 2: Introduction to Fundamental Group

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Playlist: • Algebraic Topology
We give a quick review of group theory then discuss homotopy of paths building up to the definition of the fundamental group.
Presented by Anthony Bosman, PhD.
Learn more about math at Andrews University: www.andrews.ed...
In this course we are following Hatcher, Algebraic Topology: pi.math.cornel...

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30 сен 2024

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Комментарии : 38

@-minushyphen1two379 Год назад

00:00 Review of groups, homomorphisms, and isomorphisms 18:45 Return to topology: path homotopy 22:55 Why must two paths with the same endpoints in R2 be homotopic? 30:20 Homotopy is an equivalence relation 42:15 Different equivalence classes of paths in the annulus 45:20 Loops 58:00 definition of the fundamental group

@gustavogonzalez7707 Год назад

Wonderful lecture.

@rolandscherer1618 Год назад

The topic was didactically perfectly motivated. Thank you very much!

@ompatel9017 11 месяцев назад

Gem

@Spacexioms Месяц назад

I just don’t get the example at 43:01. Wouldn’t f & g be homotopic to each other since they have the same start & end point?

@joshuad.furumele365 8 месяцев назад

Another excellent lecture! Thanks

@imthebestmathematician7477 11 месяцев назад

Thank you

@XrcyhikUbhdfbjdf 23 дня назад

Hernandez Charles Rodriguez Mary Walker Edward

@forheuristiclifeksh7836 5 месяцев назад

18:29 surjection=onto= heat everything to image. Onetoone. Man to one. Bikection

@unixux 2 месяца назад

That’s some of the best looking annulus in NA

@parthanpti 2 месяца назад

Great..... lecture.... Its a key to entering in the modern mathematics

@hyornina 10 месяцев назад

39:59 😂😂

@joshuad.furumele365 8 месяцев назад

I see you, and i raise you 29:03

@turtle926 7 месяцев назад

I raise further with 44:44 😎

@tahacasablanca5276 2 месяца назад

Nice suit and nice lecture! Thanks.

@richardchapman1592 7 месяцев назад

In attempting to use topology in sociological circumstances, are therrighte different winding numbers for thought streams of what are commonly termed the

@John-js2uj 5 месяцев назад

What on earth are you trying to say?

@richardchapman1592 5 месяцев назад

@@John-js2uj have an egoistic humility that my partial understanding can use these precise mathematical concepts in the imprecise social sciences. Worries me tho that mathematics applied to human circumstance can lead to a kind of cyber fascism if AI is taken too far too fast.

@John-js2uj 5 месяцев назад

@@richardchapman1592 You’ve got to be a bot

@richardchapman1592 5 месяцев назад

@@John-js2uj so trained in logic and emotionally damaged couldn't refute that unless you saw me in flesh and blood.

@richardchapman1592 5 месяцев назад

@@John-js2uj would ask of you an email address so I could send you a photo that you could possibly accept as not a fraud, but then there are Trojan horses on mails to worry about.

@kirillshakirov9453 Месяц назад

Great video

@hanselpedia 4 месяца назад

Thanks, lots of stuff explained in a intuitive way

@xanderlewis 6 месяцев назад

45:00 “When I use a word, it means just what I choose it to mean - neither more nor less.” - Humpty Dumpty. You can tell Lewis Carroll was a mathematician.

@richardchapman1592 7 месяцев назад

Can you make a loop that approaches infinity or indeed any surface that approaches the infinities of it's orthogonality plus one?

@wipetywipe 10 месяцев назад

Great lecture. Camera work needs improvement.

@forheuristiclifeksh7836 5 месяцев назад

17:11

@bengrange 3 месяца назад

at 39:00, when you said f and g are homotopy equivalent, did you mean to say homotopic?

@bengrange 3 месяца назад

and at 53:16, you meant "equivalence classes" not relations. Thank you for the great lectures!!

@paulwary 10 месяцев назад

At 24:30, the explicit linear interpolation formula is given for one possible homotopy, to show that there is always a homotopy of paths in R2, correct? The language suggest that this is THE homotopy (ie the one and only)

@enpeacemusic192 4 месяца назад

I think so, yeah, homotopy of paths is ány continuous deformation of paths afaik

@richardchapman1592 7 месяцев назад

Last comment on my editor needed a vector from the centre of a word to the end.

@richardchapman1592 Месяц назад

Watching the video again, it is not clear if the lines between s on f(t) are straight in R2. Some explanation of their continuity as s and t vary would help especially in spaces other than R2.

@forheuristiclifeksh7836 5 месяцев назад

6:10