NON-UNIFORM LATTICES ON UNIFORM TREES 15
(9) Theorem ([BK] 2.4) Finite grouping theorem. An indexed graph (A,i) admits
a finite grouping if and only if (A,i) is unimodular and has bounded denominators.
In the notation of (7) above, we define the volume of an indexed graph (A, i) at a
basepoint ao 6 VA\
do) V-OW,M) = £ ^ - = £ (^ )
a£VA ( ) aeVA
Aa0J
and we have the 'change of basepoint formula' ([BL] 2.6 (12)):
(11) Vola.0(A,i)=^j^Volao(A,i)
so the finiteness of the volume Volao(A,i) is independent of the choice of basepoint.
Previous Page Next Page