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| Zieschang H. — Surfaces and Planar Discontinuous Groups |
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| Предметный указатель |
1-cells, 2-cells 300
2-bridge knot 22
Accessible 294
Accola 159 167
Algebraic neighbours 143
Algebraic type 120
Alternating product 177
Angle measure 245
Annulus 72
Arc element 246
Automorphism 109
Automorphism of finite order 110
Automorphism, orientation-preserving 109
Automorphism, orientation-reversing 109
Baer 206 216
Basis for a Teichmueller 252
Basis for a theory 255—263
Bifurcation 69 179
Binary product 179
Binary product related 180
Binary product simple 184
Binary product, decomposable 184
Binary product, homotopic 184
Binary product, length of 185
Binding tie 50
bing 307
Birman 237
Boundary 44
Boundary paths 37
Braid groups 230
Braids 199
Branched covering 73
Branching number 74
Cancelling pair 185
Cancelling partner 185
Canonical dissection 70
Canonical normal form 70 114
Canonical polygon 261
Canonical presentation 71 119 139
Cayley diagram 145
Chain 44
Choise functions 27
Classification of disc, groups 120 125—128
Classification of surfaces 71
Closed surface 72
Collins 63
Combinatorial isotopy 205
Commutator hexagon 274 279—280
Commutator surface 273
Complex, 2-dimensioml 37
Congruent polygon 261
Conjugacy problem 3 59 123—132 205
Connectivity number 6
Contraction of vertices 65
Covering 7 39—42 79
Covering transformation 40
Covering, branched 73
Cross cut 294
Cross ratio 244
CYCLE 44
Cyclically reduced 3
Decomposition of disc, groups 140
Defining relations 19
Degree of a vertex 4 74
Dehn 132 194
Dehn twist 229
Description of to  85
Dilatation 264
Direction, positiv, negativ 85
Discontinuous 247 113
Disk 72
Distance 245
Doubly-convex 256
Dual 116
Dunce’s hat 62
Edges 4
Edges, geometric 4
Elementary transformation (process) 37
Elliptic transformation 245
END 244
End cut 294
Epstein 216 214
Equivalent 112 113
Euler 5
Euler-characteristic 39
Existence of disc, groups 122—125
Face 37
Face, geometric 37
Factor of binary products 179
Fenchel 132 231 283
Finite groups of mapping classes 231 233
Formal partner 185
Fox 132
Free commutator surface 273 277—279
Free group 2
Free group, isomorphic 12
Free group, subgroups of 9 12
Free product 31
Free product with amalgamation 31—35
Funcke 21 58
Fundamental domain 114 115
Fundamental group 6 37 47
Fundamental group of a covering 7
Fundamental group of a graph 6
G-equivalent 232
G-fiber 232
G-isotopy 232
Galois field 133
Generators 19
Genus 71
Geodesic 255
Geodesic dissection 255
Geometric 4
Geometric isomorphism 120
Gilinan 165
Glide reflection 245
Graph 4
Graph, connected 4
Group, dihedral 122
Group, dodecahedral 122
Group, octahedral 122
Group, tetrahedral 122
Grushko 48
Harvey 159 237
Hemes 79
Hendriks 140
Hilden 237
HNN-construction 60
HoirotoDy class 95
Holomorphically equivalent 252
Homology class 45
Homology group 44
Homomorphism class 94
Hopf 98
Hurwitz 157 155 162
Hyperbolic transformation 245
Initial subword 9
Intersection number 88
Isomorphism 40
Jordan domains 287
Jordan-curve-theorem 106 287
Kernel 185
| Klein bottle 72
Kneser 74 196
Kneser’s formula 73
Kurosh 35
Kurosh theorem 43
Length 10
Lickorish twists 229
Line 107 244
Linear fractional transformation 244
Locally path connected (lc) 291
Lyndon 132
Macbeath 132 204 283
Maclachlan 159 237
Magnus 54 199
Magnus conjecture 58
Manifold 243
Mapping  45
Mapping class group 228—231
Mapping matrices 19 3
Marked Riemann surface 252 266
Massey 84
Mennicke 132
Milnor 307
Modular problem 251
Module 244
Moebius strip 72
Moise 307
Newman 287
Nielsen 10 78 132 165 194 231 247 283
Nielsen method 10—12 51—53
Nielsen process 10 11
Nielsen properties 11 181
Non-Euclidean plane 244
Normal form 32 68 114
Null homology 44
Number of neighbours 144
Orientable 71
Parabolic transformation 245
Pasting together 48
Path 4
Path, closed 4
Path, reduced 4
Peczynski 171
Piecewise-linear 243
Planar discontinuous group = planar group 113
Planar group presentations 144
Planar net 107—109
Poincare model 244
Presentation 19
Presentation, staggered 55
Projective plane 72
Quasiconformal mapping 113
Quasilinear 295
Quotient surface 113
R-equivalent 27
Rado 64 243 304
Rank 2 24 49 170
Rank, geometrical 172
Reduced 3
Reflection 11 245
Reidemeister 9 13 24 132
Reidemeister — Schreier methods 24
Reidemeister — Schreier rewriting process 150
Related complex 37
Relations 19
Relations, consequence 20
Relations, defining 19
Riemann 157
Riemann surfaces 243
Riemann surfaces, marked 252
Riemann surfaces, moduli of 244
Root 143
Rosenberger 53 171
Rotations 110
Schreier 9 24
Schreier condition 9
Schreier representatives 9 24
Seifert 73 196
Selberg-lemma 132
Semilinear 243
Sequence of neighbours 144
Serre 168
Siegel 157 247 282
Simple curves 85—87 106 206—214
Simply-connected 109
Small cancellation theory 132
Space of canonical polygon 273 281—283
Sphere 68 72 84
Spur 4 6
Stailings 48
Star 65
Star, closed 65
Star, simple 65
Stoecker 79
Subdivision 38
surface 65 243
Teichmueller space 252
Theorem on coverings 8
Theorem on marked Riemann surfaces 266
Theorem on triangulation of surfaces 304
Theorem subgroups of free groups 9
Theorem, Alexander-Tietze 215
Theorem, Baer 206 214
Theorem, Baer — Nielsen 233
Theorem, Dehn — Nielsen 78 194
Theorem, finite mapping classes 231
Theorem, Freiheitssatz 54
Theorem, Grushko 48
Theorem, Hauptvermutung 304
Theorem, Hurwitz, Siegei 157
Theorem, Jordan curve 106
Theorem, Kurosh 35
Theorem, Massey, Heimes, Stoecker 79
Theorem, Rado 243
Theorem, Riemann mapping 250
Theorem, Rienann — Hurwitz formula 250 155
Theorem, Schonflies 299 303
Theorem, Seifert van Kampen 47
Tietze 20
Tietze transformation 20
Torus 72
TREE 5
Tree, minimal spanning 13
Type A, B 119 122
Unfree 275—277
Uniformly locally path connected (ulc) 291
Universal property of free groups 2
Value 179
Van der Waerden 32
Vertex 4
Vertex, boundary 65
Vertex, inner 65
Whitehead 14
Whitehead automorphisms 14
Wiman 157
Word 1
Word problem 2 3 59 128—132 205
Word, cyclically reduced 3
Word, equivalent 1
Word, product of 1
Word, reduced 3
Zieschang 170 196 204 214 237
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