Timeline for Reference request: The geometry of $GL_2(\mathbb{R})$ and related questions

6 events

when toggle format	what		by	license	comment
Dec 6, 2011 at 7:46	answer	added	Asaf		timeline score: 1
Dec 5, 2011 at 23:50	comment	added	paul garrett		About infinite volume (as raised by @Jim H.): this is a genuine issue for "Fuchsian" subgroups of SL(2,R), and more generally for real-rank-one groups to which (Mostow-Margulis-Zimmer) rigidity does not apply. One could already declare that one's only interest was in arithmetic subgroups (congruence-or-not), in which case volumes are always finite. Nevertheless, indeed, there is a substantial school of investigation concerning non-finite-co-volume discrete subgroups of SL(2,R), SL(2,C), and SO(n,1)'s more generally. (I don't know/understand the sensibilities/goals of that.)
Dec 5, 2011 at 23:34	comment	added	Jim Humphreys		Borel's softcover book Introduction aux groupes arithmetiques (Hermann, 1969) is helpful for fundamental domains (though it still has notational inconsistencies after he spliced two older sets of lecture notes). For some special cases I tried to write this down in Borel's style but in English in my Springer Lecture Notes 789 Arithmetic Groups. In general, the volume of a fundamental domain will be infinite.
Dec 5, 2011 at 20:34	answer	added	paul garrett		timeline score: 3
Dec 5, 2011 at 20:16	comment	added	Alain Valette		I suggest Siegel's "Lectures on the geometry of numbers", lectures XIV and XV
Dec 5, 2011 at 20:12	history	asked	Frank Thorne	CC BY-SA 3.0