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Homework Help: SO(3,1) Connectedness problem

  1. Feb 25, 2010 #1
    define the group
    [itex]S0_O(3,1) = \{ a \in SO(3,1) | (ae_4,e_4) < 0 \}[/itex]
    i need to show this group is connected

    in my notes it says a group G is connected if it satisfies any of the following:
    (i)any two elements of G can be joined by a [itex]C^k[/itex]-path in G
    (ii) it is not the disjoint union of two non-empty open sets
    (iii) it is generated by a neighbourhood of 1 (the identity matrix)
    (iv) it is generated by [itex]exp \mathfrak{g}[/itex]

    im not sure which one to try and prove or how to go about it really. can anybody offer some advice? thanks.
  2. jcsd
  3. Feb 26, 2010 #2
    Re: Connectedness

    I don't know enough about SO(3,1) to figure out the answer, but another potential way to show it connected is to show it's the image of a known-connected space under a continuous map.
  4. Feb 27, 2010 #3
    Re: Connectedness


    ive got a feeling its going to be a proof by contradiction but that might be a whole load of rubbish.
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