homotopy groups

  • What is \pi_1(X)?

homotopy classes of maps S^1\to X

  • What is \pi_2(X)?

  • What is \pi_n(X)?


  • \pi_3(S^2)=\mathbb{Z}, the hopf number
  • \pi_4(S^3)=\mathbb{Z}_2

11 responses to “homotopy groups

  1. Alberto

    Also, zeigen, dass S^3 homohomorph zu SU(2) ist, ist ganz einfach und ich habe schon das gemacht!

    Zum Beispiel, Pi_4(S^2)=Pi_4(S^3)= \mathbb{Z}_2 zu zeigen. Ich zeigte schon \Pi_1 (SO(3)) = \mathbb{Z}_2, wills du die Lösung anschauen?

  2. c-qit

    Wilson loops and Chern-Simons Th.

    Click to access 0911.2687v1.pdf

  3. Alberto

    Yes, I’m going whit you next week.
    Congratulations on your 1000 visits! we celebrate with quality issues, or what dou you thynk?

    I find especially in the homotopy groups great application to Feyman-Path Integral: Frau De Witt-Morette.


  4. v-ki

    cada mapa f:S^3\to S^2 tiene asociado un “link” y el “linking number” es un invariante homotópico para f

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