Computing homology groups | Algebraic Topology | NJ Wildberger

22 Comments

  1. ZAID SSERUBOGO said:

    Please don't intefear in my evolutionary patters, you make lose the smoothness and continuity of its flow! But thanks for great work

    May 25, 2019
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  2. John Stroughair said:

    Very clear explanation – thanks!

    May 25, 2019
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  3. Lukáš Sladký said:

    I'm just doing an algebraic geometry course on Erasmus and this really helped me to filled my lack of knowledge in tolopology needed for the class.

    May 25, 2019
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  4. Soroush Pakniat said:

    Thank you

    May 25, 2019
    Reply
  5. Tanika Soni said:

    sir, can you please send the link for finding triangulations of polyhedra if there is any

    May 25, 2019
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  6. midevil656 said:

    Thanks!

    May 25, 2019
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  7. Reiner Wilhelms-Tricarico said:

    I love it. Wildberger saves us from the dreary task of grinding through the usual tomes on this subject, where the authors seem to believe that drawing a single picture would make the subject somehow less glorious 🙂

    May 25, 2019
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  8. Mohammad Bazzi said:

    Thanks for the video. I would actually like to know why you considered (x z) to be equal to – c. Clearly it is the difference in orientation, but is there an argument which would work for higher dimensions?

    May 25, 2019
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  9. Ram Datt Joshi said:

    Absolutely impressive! I am wondering if it is possible to post the videos for like: PL Gauss-Bonnet theorem, and about chain derivation results. Thank you for your generosity and your support!!!

    May 25, 2019
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  10. Udit Gupta said:

    This is exactly what I was looking for. It was a bit abstract and now it makes perfect sense, roughly the dimension of a homology group counts the number of cycles that aren't boundaries. This equivalently measure how many "holes" there are of r-dimension in the space.
    Very cool, Thanks!

    May 25, 2019
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  11. Tien Le said:

    Great lecture. Thanks!

    May 25, 2019
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  12. MarcoGorelli said:

    MASSIVE thank you for uploading this. It's so much clearer to me now.

    May 25, 2019
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  13. Hwi Lee said:

    really love it,Thanks

    May 25, 2019
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  14. Dustin Bryant said:

    +njwildberger I am in an algebraic topology course that essentially starts from your 35th video (intro to homology) and we are reading hatcher which is good but I find it too verbose, are there any (modern & friendly) books you would recommend on the subject? By the way, I really have enjoyed watching these videos the subject has really come alive and I'm able to appreciate the abstract setting with your great examples.

    May 25, 2019
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  15. Carina Vrrumm said:

    thanks, this video helped a lot!

    May 25, 2019
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  16. The Cat Crusader said:

    Highly useful lectures, thanks! As I understood you used the argument that a map is injective if it is non-zero on generators. Can this always be applied in the setting of homology? I was thinking of the projection from the integers onto Z/2Z as a counterexample…

    May 25, 2019
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  17. Insights into Mathematics said:

    The del-zero map is always zero, since there is no chain group of dimension -1.

    May 25, 2019
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  18. Insights into Mathematics said:

    This is true—here is a good problem: after you have finished watching this video and the next, see if you can compute the homology groups of the Klein bottle.

    May 25, 2019
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  19. relike868p said:

    And could you give an example where the del-zero map is not a zero map?

    May 25, 2019
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  20. relike868p said:

    But how do you define the del-zero map?

    May 25, 2019
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  21. relike868p said:

    By the way, you have not given any problem sets (or do you) in these several lectures…..

    May 25, 2019
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  22. جخ said:

    Awesome video! Thanks!

    May 25, 2019
    Reply

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