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| Goresky M., MacPherson R. — Stratified Morse Theory |
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| Предметный указатель |
Local Morse data and main theorem 65
Local Morse data and moving the wall 91
Local Morse data in nonsingular case 73
Local Morse data is Morse data 95
Local Morse data, definition of 63
Local Morse data, independent of choices 92
Local Morse data, intuition 60
Lojasiewicz, S. 34 35 43 44
Lysternik, L. 21
MacPherson, R. 29 46 48 66 132 147 150 153 161 164—169 208—222
Maigrange 224
Main theorem, proof of 100
Manifold collection 34
Massey, D. 178
Mather, J. 35 37 38 41 42 56 140 220
Mazur, B. 21
Merle, M. 45 160
Metric, Finsler 226
Micro-solutions 224
Microlocal 17
Milnor fibration 134 161 165
Milnor, J. 56 64 65 73 128 134 152 154 159 164 165 219
Minimax principle 21
Moebius function 238 239 252
Monodromy and normal Morse data 159 166
Monodromy and variation 210
Monodromy, definition of 139 167
Monodromy, independent of choices 140
Monodromy, trivialization of 143
Morphism, local complete intersection 154 200 229
Morse data of complex varieties 16 159 173
Morse data, coarse, definition of 62
Morse data, definition of 62
Morse data, embedding of 100
Morse data, homotopy 62 122 173
Morse data, intuition 4
Morse data, local and main theorem 65
Morse data, local and moving the wall 91
Morse data, local in nonsingular case 65 73
Morse data, local, definition of 63
Morse data, local, independent of choices 92
Morse data, local, intuition 60
Morse data, nonproper 120
Morse data, nonsingular case 65 73
Morse data, normal 8 64
Morse data, normal and complex link 16 159 166
Morse data, normal and halfiink 98 166
Morse data, normal and monodromy 166
Morse data, normal and normal slice 97
Morse data, normal of complex varieties 16 159 166
Morse data, normal of two functions 128 169
Morse data, normal, definition of 8 64
Morse data, normal, homotopy 122
Morse data, normal, independent of choices 93
Morse data, normal, punctured 180 186
Morse data, of complex varieties 16 159 173
Morse data, relative 115
Morse data, relative nonproper 124
Morse data, relative normal, complex case 168
Morse data, tangential and moving the wall 91
Morse data, tangential, definition of 8 64
Morse data, tangential, independent of choices 92
Morse data, tangential, nondegenerate case 65 73
Morse function and topological stability 13 34 52
Morse function and transversalily 51
Morse function on a stratified space 50 52
Morse function, classical 12
Morse function, existence of 53
Morse function, nonproper 10 119 147 168 174 245
Morse function, perfect 236 248
Morse group and characteristic variety 224
Morse group and intersection homology 211
Morse group, vanishing of 212
Morse index and intersection homology 18
Morse index and Levi form 190
Morse index and tangential Morse data 73
Morse index, classical 5 64
Morse inequalities 18 219
Morse theory of many Morse functions 142
Morse theory relative 11 12 114
Morse theory, complex 15
Morse theory, equivariant 11
Morse theory, nonproper 10 12 17
Morse theory, relative and nonproper 124
Morse theory, stratified 3
Morse, M. 3 19 21 22 39 51 53 54 64 73 173
Moving the wall 71
Moving the wall, example of 71 74
Moving the wall, intuition 70
Nakai, I. 42
Narasimhan, R. 152
Nash blowup 45
Navarro Aznar, V. 45 160
Neighborhood retraction 220
Neighborhood, cylindrical 132 162
Neighborhoods of analytic sets 206
Nondegenerate covector 44 160
Nondepraved critical point, definition of 54 55
Nondepraved critical point, independent of coordinates 58
Nondepraved critical point, intuition 50
Nondepraved critical point, properties of 57
Nonproper Morse function 10 119 147 168 174 245
Normal defect, definition of 178 176
Normal defect, estimates on 180
Normal defect, intuition 176
Normal Morse data and complex link 166
Normal Morse data and cylindrical neighborhood 135
Normal Morse data and halllink 67 98
Normal Morse data and main theorem 65
Normal Morse data and monodromy 166
Normal Morse data and normal slice 66 97
Normal Morse data for complex varieties 159
Normal Morse data for two complex functions 169
Normal Morse data of many Morse functions 142
Normal Morse data of two Morse functions 128 135
Normal Morse data, definition of 8 64
Normal Morse data, finitely many possibilities 95
Normal Morse data, independent of choices 65 93
Normal Morse data, punctured 180 186
Normal Morse data, relative, complex case 168
Normal projection data 160 163
Normal slice and Morse data 66 97
Normal slice, characteristic covectors of 84 129
Normal slice, definition of 7 41
Normal slice, local structure of 134 165
Normally nonsingular map and transversality 47
Normally nonsingular map, definition of 46
Nullity 192
Ogus, A. 154 177
Oka, M. 154
Okonek, C. 226
Order complex and homotopy equivalence 243
Order complex, definition of 237
Ordinary critical point 119
Orlik, P. 235 238 239 251
Orro, P. 45 52 53
Osgood, W.F. 34
Pappus 257
Particular neighborhood 132
Perfect Morse function 236 245 248
Perverse sheaf 212
| Perverse sheaf and  -modules 224
Perverse sheaf, definition of 224
Perverse sheaf, specialization of 220
Perversity, logarithmic 212
Perversity, middle 209
Perversity, sublogarithmic 212
Picard — Lefschetz theorem 28
Picard, E. 29
Pignoni, R. 13 50 52—54 182 184 196—197 228
Poincare, H. 20 21 29 33
Polar variety 161
Positive vectorbundle 226
Projective space, complements of 252
Projective subspaces, homology of 239
Projective transformation, and transversality 39
Punctured normal Morse data 180 186
Pure sheaf 223
Pythagorus 81
q-convexity 225
q-defective pair, definition 225
q-defective vectorbundle 226
Quartering and complex link 128
Quartering and halflink 135
Quartering, definition of 131
Quartering, relative 141
Quasiprojective variety, and Lefschetz theorem 24 153
Rectified homotopical depth 153 185
Relative halflink 116
Relative Lefschetz theorem 25 150
Relative Morse data 115
Relative nonproper Morse theory 124
Relative normal Morse data, complex case 168
Relative theory 114
Restricted Levi form 192
Restricted signature 191
Retraction, of a neighborhood 220
Riemann, B. 20 28
Robbins, H. 39 51
Roberts, J. 26
Rota, G.C. 238 252
Roundling the corner 109
Sabbah, C. 224
Saito, M. 29
Sans eclatement mapping 34
Sard's theorem and existence of Morse functions 51
Sard's theorem and transversality 40
Sard, A. 40 51
Schapira, P. 212 223 224
Schnirelmann, L. 21
Schubert variety 213 231
Schwartz, L. 34
Semianalytic set, definition of 43
Semianalytic set, stratification of 43
Semismall map, and Lefschetz theorem 25 151
Serre, J.-P. 29
Setup, nonproper Morse 11
Setup, relative Morse theory 12
Sheaf theory, and Morse theory 222
Siersma, D. 22
Signature, restricted 191
Simart, G. 29
Singularity defect, definition of 185
Singularity defect, intuition 177
Smale, S. 3 21 64 73
Small map, and Lefschetz theorem 151
Small resolution 231
Solomon, L. 235 238 239 251
Sommese, A. 149 180 192 207 225 226
Soroni, G. 188
Specialization map and -modules 224
Specialization map and perverse sheaves 224
Specialization map, definition of 117 220
Specialization map, fibres of 221
Specialization map, of perverse sheaf 220
Stasica, J. 43
Steenrod, N. 209
Stem space 15 17 148 152
Stem space, intersection homology of 26 216
Sternberg, S. 51
Stratification of subanalytic sets 43
Stratification, definition of 37
Stratification, historical remarks 33
Stratification, intuition 6
Stratification, local structure 40
Stratified map see “Thom mapping”
Stratified map and semianalytic maps 43
Stratified map, counterexamples 231
Stratified map, definition of 42
Stratified Morse theory, part A 6 62 90
Stratified Morse theory, part B 8 65 100
Stratified submersion 41
Subanalytic map, stratification of 43
Subanalytic set, definition of 43
Subanalytic set, stratification of 43
Subanalytic set, tangents to 44
Submersive family, definition of 39
Subvariety, complement of 1
Switzer, A. 178
Tangent space, generalized 44 128 160
Tangential defect intuition 176
Tangential defect, estimates on 179
Tangential Morse data and moving the wall 91
Tangential Morse data, definition of 64
Tangential Morse data, independent of choices 92
Tangential Morse data, nonsingular case 65 73
Tangents, to an analytic set 44
Teissier, B. 45 158 160 161 164 165
Thom mapping 34 136 170
Thom, R 15 21 22 29 34—35 37 41—13 48 51—53 56 64 101 136 152 154 170 173 220 231
Thomason, R. 235
Transversalily and Morse functions 51
Transversalily and normally nonsingular maps 47
Transversalily of stratified spaces 38
Triangulation, of Thom mapping 34
Trotman, D. 35 38 45 52 160
Tubular neighborhood, and control data 42
Vanishing cycles 223
Variation map 210
Veblen, O. 20 33
Vectorbundle, ample 226
Vectorbundle, q-defective 226
Verdier, J.L. 43
Verona, A. 37
Vertical part, of link 132
Villani, V. 188
Vilonen, K. 169
Wachta, K. 43
Wall, intuition 70
Wallace, A.H. 29 56
Weidner, H.G. 154
Whitehead, J.H.C. 33
Whitney conditions, definition of 37
Whitney conditions, historical remarks 35
Whitney stratification and exceptional points 45
Whitney stratification and faults 45
Whitney stratification, definition of 37
Whitney stratification, historical remarks 33
Whitney stratification, intuition 6
Whitney stratification, local structure 40
Whitney topology 12 38 53
Whitney, H. 33—37 40 44 50—53
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