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Dicks W., Dunwoody M.J. — Groups acting on graphs |
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Предметный указатель |
, , , group 155
, , , module 144
(, )-weight 197
(-) module 28
(-)action 3
(-)compressible (-)set 90
(-)compressible (-)trec 90
(-)compressible edge 90
(-)finite 4
(-)free (-)set 3
(-)incompressible, (-)set 90
(-)incompressible, (-)tree 90
(-)incompressible, edge 90
(-)isomorphic 3
(-)linear map 28
(-)map 3
(-)orbit 3
(-)retract 73
(-)set 3
(-)set, right 3
(-)stabilized 3
(-)stabilizer 3
(-)stable 3
(-)subgraph 4 5
Accessible 130
Acyclic 141
Adjacent 57
Affinely independent 216
Almost (-)stable 48
Almost all 59
Almost equal 48
Almost equality class 48
Almost equality class, for a tree 74
Almost finitely presented (afp) group 229
Almost Stability Theorem 74 99
ARC 243
Aspherical 135
atoms 54 62
Attaching maps 79
Augmentation, homomorphism 111
Augmentation, ideal 111
Augmentation, map 29 115
Augmentation, module 29 115
Augmented cellular chain complex 29
Automorphism group 21-8
Automorphism of free group 24 37-8
Automorphism of graph 5
Automorphism, affine 28
Automorphism, de Jonquires 28
Band 227
Band, twisted 227
Band, untwisted 227
Base of fibred tree 79 80
Blowing up 78-80
Boolean ring 54 124
Boolean ring of graph 54
Boolean ring of group 126
Boolean space 124
Boolean space of graph 124
Boolean space of group 126
Boundary 138 141
Boundary irreducible three-manifold 258
Boundary map 29
Cap product 146-7
Cayley graph 5
Cellular chain complex 29
Chain of Type B 251
Chain of Type C 253
Chain of Type D. 253
Chain, equivalence 141
Chain, inverse 141
Chain, map 141
Changes of Type A 250
Chararcteristic of ring 206 (see also Euler chararcteristic)
Clopen 124
Closed munifold 135
Closed path 8
Coboundary 54
Cocomplex 141
Cohomological dimension 110
Cohomology of group 107 135 157
Cohomology of pair 138 176
Coinduced module 107
Commute with direct limits 143
Compatible patterns 235
Complete graph 67
COMPLEX 29 141
Component of function 54
Component of graph 9
Component of set of edges 88
compress 90
Compressing disc 260
Concatatation of paths 8
Concatatation of words 1
Concentrated 141
Conjugation 3
Connected element of Boolean ring of graph 55
Connected graph 9
Connected relation in graph 9
Connected set of vertices in graph 55
Connecting elements 11
Connecting map 142
contracting 9
Contracting, map 9
Costructure map of tree 48
Countably generated over a subgroup 82
Covering map 221
cube 41
Cut 54
CYCLE 141 218
Cyclic group 2
Degree 141
Derivation 30
Derivation, inner 31
Derivation, outer 31
Derived complex 217
Diagonal -action 3
Diagonal map 179
Diagonal set 42
Differential 141
Dihedral group 2
Dimension, Cohomological 110
Dimension, duality 136 139 152 156 158 175 177
Dimension, projective 110
Disc equivalent one-submanifolds 243
Disc equivalent two-submanifolds 254
Distance in tree 8
Distance in unoriented graph 67
Distance-transitive 67 71
Doubly infinite path 18
Dual map 47
Dual of CW-complex 161 164
Dual of linear map 149
Dual of module 149
Dual of Poincar module 152
Duality see Poincar and geometric duality
EDGE 4
Edge, function 11
Edge, group 11
Edge, set 4
Empty path 8
Ends of graph 124
Ends of group 126
Ends, more than one 128
Ends, two 129- 30
Essential vertex 232
Euler characteristic 36 105 163
Exact complex 29
Ext 142
Exterior element 62
| Fibre 79 80
Fibred tree 79 80
Finitely generated group over a subgroup 82
Finitely generated projective resolution 144
Forest 9
Free Abelian group 21 28
Free action on set 3
Free action on tree 16
Free algebra 28
Free factor 123
Free generators 2
Free group 2
Free object 21
Free product 14
Free product, with amalgamation 14
Fundamental (-) transversal 10
Fundamental class for group 157
Fundamental class for module 152
Fundamental class for pair 176
Fundamental domain 220
Fundamental group of a graph 13 36
Fundamental group of a graph of groups 13 32
Fundamental group of a topological space 220
GD see Geometric duality
General linear group 21-8 106
Generate Boolean ring 54
Generate group 1
Generate subgroup 2
Generate subtree 8
Generating set 1
Generators 2
Geodesic in tree 8
Geodesic in unoriented graph 67
Geometric duality, group 136 158
Geometric duality, pair 139 177
Geometric realization 5
Going into 5
Going out of 5
Graded abelian group 141
Graded map 141
Graded over -set 179
Graph 5
Graph of groups 11
Graph of groups, associated to (-)graph 11
Graph, (-) 4
Graph, automorphism of 5
Graph, complete 67
Graph, directed multi 45
Graph, isomorphism of 5
Graph, map 5
Graph, unoriented 67
Grushko — Neumann theorem 45
HNN extension 14
Homogeneous 141
Homology 141
Homology, for group 135 157
Homology, for pair 138 176
Homology, for simplicial complex 219
Homology, on paths 8
Homotopy 141
Inaccessible 130
Incidence functions on edges 4
Incident to 4
Index of subgroup 3
Indicable 207
Induced module 107
Infinite path 18
Initial vertex of edge 4
Initial vertex of path 8
Interior element 62
Inverse of path 8
Inverse of word, I invertible on 115
Involution 155
Irreducible three-manifold 258
Kaplansky’s Theorem 203
Kronecker product 219
Kurosh subgroup theorem 35
Lattice 25 59
Left conjugation 3
Length of path 8
Lift 142
Locally finite graph 5
Loop 4
Maximal subtree 11
Minimal (-)subtree 20
Neighbour of vertex 5
Neighbourhood of vertex 5
nested elements 47
Nested subset 48 53
Nielsen — Schreier theorem 37
Normal form 45
Normal surface 248
Occur in path 8
Opposite 57
Orbit space 220
Orientable 136 139 157 176
Orientation, involution 156 176
Orientation, map 136 156 176 177
Orientation, module 156 175
Partition for a function 88
Path 8
Path, closed 8
Path, doubly infinite 18
Path, empty 8
Path, infinite 18
Path, inverse 8
Path, reduced 8
Path, simple closed 8
Pattern 224
Pattern, equivalence 225
Pattern, reduced 228
Patterned surface 246
pd see Poincar duality
Piece 249
Planar Group 162
Poincar duality for manifolds 135
Poincar duality group 136 156
Poincar duality module 152
Poincar duality pair 139 175
Point, away from 18
Point, in opposite directions 18
Point, in same direction 18
Point, to 18
Polyhedron 216
Polynomial ring 28
Presentation 1
Projection map 179
Projective (-) module 109
Projective complex 142
Projective dimension 110
Projective linear group 21 24 103 106
Projective module 110
Projective resolution 110 142
Projective special linear group 21 24 106
Proper action 136
Quotient graph 5
Quotient set 3
Rank of graph 36
Rank of group 2
Realization of a graph 5
Realization of a simplicial complex 217
Reduced path 8
Refine 87
Relation set 2
Relations 2
Relators 2
Respect nesting 49 53
Returning arc 250
Right -set 3
Right conjugation 3
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