1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Connectedness problem Date
Path-connectedness for finite topological spaces May 16, 2017
Struggling with arc-connectedness Oct 26, 2015
Connectedness math problem Apr 18, 2011
A local path connectedness problem Oct 18, 2010
Connectedness math problem May 8, 2008