1
$\begingroup$

I would like to know the motivation of the geometric argument applied on a 'fundamental domain' to get the generators of $SL_2(\mathbb{Z})$. In particular, are there easier examples where this sort of proof works.

  • 0
    You need to be more specific about what argument you're talking about. – 2017-02-09
  • 0
    By Geometric argument, I mean the argument on the fundamental domain of upper half plane. For instance, in Serre's book A course in Arithmetic, I have seen that we use this fundamental domain to prove that S and T are the generators. I would like to see more examples of finding generators by looking at a 'subgroup' acting on a 'space'. – 2017-02-15

1 Answers 1

0

I recommend that you look at Serre's book Trees, which discusses arguments of this sort, and related theory.