pretrivial element, 13
pretrivial turn, 13
takes place in
Zo,
40
turn, 13
forest groupoid, 7
forest, 6
free,
action on tree, 16
category, 33
group, ii
groupoid, 7
on a graph, 9
G-set, 5
full,
subgraph, 6
subgroupoid, 7
functor, 7
Gaboriau, D., 1, 2, 46
generate, 7
Gersten, S.M., 1
Goldstein, R.Z., 2, 16, 23, 72
graph, ii, 5
abstract map, 10
automorphism, 6
core, 6
core of, 6
empty, 6
endomorphism of, 6
finite, 6
metric, 31
morphism, 6
covering, 6
immersion, 6
inert immersion, 21
locally injective, 6
locally surjective, 6
pullback, ii, 1, 19
reduced rank, 15
group, ii
endomorphism of, ii
automorphism of, 1
outer, 34
groupoid, ii, 6
endomorphism, 7
idempotent, 8
induced, 10
inner, 7
similar, 8
free, 7
rank, 15
reduced rank, 15
morphism, 7
associated to a G-set, 9
growth rate, 46
Handel, M., ii, 1, 2, 5, 11, 23, 32, 33, 46,
48, 58, 61, 68, 72
homotopy equivalence, 11
INDEX
idempotent groupoid endomorphism, 8
immersion, graph morphism, 6
Imrich, W., 1, 2, 19, 68
incidence functions, 5
incident, 5
indivisible fixed element, 51
induced groupoid morphism, 10
inert,
F-set,
19
graph morphism immersion, 21
groupoid morphism, 21
subgroup, 1
initial segment, 10
initial vertex, 5
injective,
7!"1,
10
inner groupoid endomorphism, 7
inner self-map, 11
invariant, 11
Inverse Limit Theorem, 22
inverse up to natural equivalence, 8
for abstract maps of graphs, 11
irreducible,
automorphism, 46
matrix, 27
for f3 modulo
Zo,
33
test for irreducibility, 33
isomorphic
F-sets,
5
isomorphism ofF-sets, 5
Jaco, W., 1
Karrass, A., 2, 22
length,
Z-, 9
f.-, 31
Levitt, G., 1, 2, 3, 46
Lipschitz number, 31
locally injective, 6
locally surjective, 6
Lustig, M. 1, 2,3, 23,46
Magnus, W., 2, 22
matrix,
for abstract map of graphs, 32
modulo
Zo,
33
dominate, 29
irreducible, 27
zero, 27
non-negative, 27
permutation, 27
positive, 27
reducible, 27
McCool, J., 1
measuring five-tuple, 34
metric graph, finite, 31
minimal representative, 46
mixed,
turn, 39
79
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