78
of graph, 6
of group, 1
irreducible, 46
outer, 34
axiom of choice, 5
basic operations, 11
see also: collapsing, folding, re-orienting,
subdividing
basically injective,
abstract map of graphs, 10
groupoid morphism, 7
basis, of free groupoid,
7
Bergman,
G.M., 1 72
Bestvina, M., ii, 1, 2, 3, 5, 11, 23, 32, 33,
46, 48, 58, 61, 68,
72
bound, cancellation, 31
Bounded Cancellation Lemma, 32
buffer, 46
cancellation, 10
bound, 31
canonical factorization
into smooth elements, 48
category, 6, 10
Cayley graph, 16
Cayley-Hamilton Theorem,
30
closed
edge, 5
groupoid element, 7
Cohen,
M.M., 1,
2, 23
collapsing,
components of forest, 11
components of forest groupoid, 8
edge, 12
pretrivial arc,
35
pretrivial edge, 12
COillponent,
of graph, 6
of groupoid, 6
composition,
7,
10
compressed, 71
conjugate, 5
conjugation, right, 8
connected, 6
continuous 10
core
graph,
6
finite, 6
of a graph, 6
covering, 6
universal cover, 24
CW-complex 5
continuous map, 10
derivative, 47
disconnected,
6
dominated,
29
duration, 47
INDEX
Dyer, J.L., 1
edge,
5, 6
closed, 5
occur, 9
of graph, 5
of groupoid, 6
open, 5
efficient map, 48
eigengroup, 24
element, of groupoid,
open,
7
closed,
7
non-trivial, 7
has turn, 10
smooth, 47
empty graph,
6
endomorphism,
of graph,
6
of group, ii
of groupoid,
7
idempotent, 8
induced, 10
inner,
7
similar, 8
equalizer, 82
equivalence,
homotopy, 11
of graphs, 11
of groupoids, 8
equivalent,
abstract maps of graphs, 11
graphs, 11
groupoid morphisms, 8
groupoids, 8
expression, 10
Feighn; M., 2, 32
finite,
graph,
6
core graph, 6
metric graph, 31
abstract map, 31
finitely
generated,
groupoid,
7
group, ii
five-tuple, measuring, 34
Fixed-point Lemma, 24
fixed,
by groupoid endomorphism,
7
by abstract map of graphs, 11
subgroup, 1
subgroupoid,
for self-map, 11
for groupoid endomorphism, 7
Folding Lemma, 13
folding, 12
in
Q(¢),
40
indivisible fixed element, 56
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