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Why Braid Group is infinite?

  1. Jul 19, 2012 #1
    Hi,
    can anyone explain me why (mathematically) the braid group is infinte? I guess it's infinite because you can do every braid you want and even if you braid two particles interchanging them twice in a clock (or counterclock) wise manner, (so you bring them back at the original positions), the system does not necessarily back to the same state. But has someone a good explanation of this fact?
    Thank you,
    gioia
     
  2. jcsd
  3. Jul 19, 2012 #2

    martinbn

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    Science Advisor

    B_1 is trivial, B_2 is infinite cyclic and B_{n-1} is a subgroup of B_n, so from the second on they are infinite.
     
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