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Bruhat-Tits Space

  1. Aug 6, 2009 #1
    Hello and thank you for your time in reading this.

    I am fairly new to this area of math and am attempting to study a beginning lecture on bruhat-tits spaces. I have some texts and lectures; however, I am having trouble finding web resources on the subject so I felt it ok to post my question.

    According to a lecture I am studying, a Bruhat-Tits Space is a complete (every Cauchy sequence converges) metric space that satisfies the semi parallelogram law.

    My understanding of the semi parallelogram law is that it follows that for some x1 and x2, there exists z such that:

    d(z,x1) = d(z,x2) = 1/2 d(x1,x2).

    Well, is this not just basically saying that a Bruhat-Tits space is a metric space such that for any two points, there exists a midpoint on the shortest path (or should I say geodesic?) between the two points?

    Is there something that I am missing? As of now I do not see how this is so extravagant compared to a standard metric space.
     
  2. jcsd
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