Goresky M., MacPherson R. — Stratified Morse Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Goresky M., MacPherson R. — Stratified Morse Theory

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Название: Stratified Morse Theory

Авторы: Goresky M., MacPherson R.

Язык:

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 272

Добавлена в каталог: 17.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$A_{1}$ (a fringed set)      82
$A_{2}$ (a fringed set)      84
$A_{3}$ (a fringed set)      85
$A_{4}$ (a fringed set)      86
$A_{5}$ (a fringed set)      88
$A_{6}$ (a fringed set)      89
$A_{f}$       see “Thom mapping”
$C(\mathscr{A})$ (complex), definition of      241
      see “halflink”
$\Delta$       see “Defect”
$\mathscr{D}$ -module      223
$\mathscr{L}$       see “Complex link”
$\mathscr{S}$ -decomposition, definition of      36
$\mathscr{S}$ -filtered space, definition of      241
Abraham, R.      39 51
Affine subspace, homology of      238
Affine subspaces, complexification of      238
Alexander, J.W.      20
Alexandrov, P.S.      237
Ample vectorbundle      226
Analytic variety, local structure of      164
Analytic variety, neighborhoods of      206
Analytic variety, stratification of      43
Andreotti, A.      29 51 52 148 152 154 80 225 226
Arnold, V.I.      235
Arrangement, central      242
Arrangement, complexification of      257
Artin, M.      151 217
Atiyah, M.F.      21
Attaching a pair of spaces      61
Baiada, E.      22
Barth theorem      27 149
Barth, W.      27
Basepoint      150
Baum P.      48
Beilinson, A.A.      208 212 220 224
Benedetti, R.      52 53
Bentini theorem      25 151
Bernstein, J.      208 212 220 224
Bertini, E.      25 151
Betti      20
Bibliography      258
BirkhofT, G.D.      21 238
Blakers and Massey theorem      178
Blakers, A.      178
Boardman, J.      35
Bott, R.      21 64 114 173 180 225 226
Bottom ( $\delta$ , $\varepsilon$ )      93
Box ( $\delta$ , $\varepsilon$ )      91 93
Braid diagram      215
Branched coverings, and connectivity theorems      27
Brieskorn, E.      235
Brown      33
Bruce, J.W.      52 93
Bruhat, F.      56
Cairns, S.S.      20
Cartan, H.      29 56
Cartier, P.      24 235
Central arrangement      242
Characteristic covector, and moving the wall      71 81
Characteristic covector, definition of      44 46
Characteristic covector, diagram of      109
Characteristic covector, of a level      130
Characteristic covector, of a map      46
Characteristic covector, of a stratified space      44
Characteristic function, definition of      78
Characteristic variety      224
Cheeger, J.      213
Cheniot, D.      37
Classical Morse theory, part A      4
Classical Morse theory, part B      5 65 73
Clemens, H.      215
Codefective pair, definition      225
Complex $C(\mathscr{A})$ , definition of      241
Complex functions, local structure of      170
Complex link and halflink      165
Complex link and normal Morse data      166
Complex link and quarterlink      128
Complex link and variation map      210
Complex link independent of choices      163
Complex link of local complete intersection      187
Complex link, bundle of      209
Complex link, connectivity of      180 186
Complex link, definition of      15 161
Complex link, homotopy dimension of      17 183
Complex link, intersection homology of      214
Complex link, intuition      15 17 128 148 159
Complex link, Morse theory of      176
Complex link, relative      168
Complex Morse theory, technical results      147
Complex stratified Morse theory, part A      16 147 174
Complex stratified Morse theory, part B      18 147 174
Complexification of affine subspace      238
Complexification of arrangement      257
Complifold      33
Conley Morse index, and Morse data      62
Conley, C.      21 62
Connectivity theorems      26 149
Conormal vector, definition of      44
Control data      42
Controlled foliation      48
Controlled lift      42
Controlled vectorfield      42
Convexity defect and Levi form      193
Convexity defect, definition of      178
Convexity defect, intuition      177
Course Morse data, definition of      62
Critical fibre      114 117
Critical point at infinity      119
Critical point, definition of      6 52
Critical point, nondepraved      50 54 55 57
Critical point, ordinary      119
Critical submanifold      21
Curve selection lemma      56
Cylindrical neighborhood      132
Cylindrical neighborhood and normal Morse data      135
Cylindrical neighborhood, conical      134
Cylindrical neighborhood, definition of      162
Cylindrical neighborhood, structure of      165
Decomposed space, definition of      36
Defect singularity, definition of      185
Defect, convexity and Levi form      193
Defect, convexity, definition of      178
Defect, dual normal, estimates on      183
Defect, fibre, definition      180
Defect, intuition      176
Defect, normal, definition of      178
Defect, normal, estimates on      180
Defect, tangential, estimates on      179
Defective pair, and Lefschetz theorem      227
Defective pair, definition of      225
Deformation to the normal bundle      48
Deligne, P.      25—29 114 150 151 208 212 217—224 235
Denkowska, Z.      43
Depth, rectified homotopical      153 185
DeRham functor      223
Diagrams, definition of      102
Distance function as a Morse function      13 51 54 148 179 245
Distance function, Levi form of      193 194
Dual normal defect, estimates on      183
Duality, and Lefschetz hyperplane theorems      27
Dubson, A.      161
DuPlessis, A.      43 56
Durfee, A.      136 159 164 170
Eilenberg, S.      20
Equisingularity      35
Equivariant cohomology      21
Exceptional point      45 160
Excision property, of Morse data      62
Excision theorem, for homotopy      178

Exhaustion function      225
Fallings, G.      26 149
Faults, and Whitney stratifications      45
Feldman, E.A.      34 35 52 226
Fibre defect, counterexamples      230
Fibre defect, definition of      180
Fibre defect, intuition      177
Fieseler, K.H.      212 216—217 226—229
Finsler metric      226
Flat, definition of      237
Folkman, J.      237 252
Fox, R.      34
Frankel, T.      29 51 148 152 154 180
Fringed set      22
Fringed set and local Morse data      91
Fringed set, definition of      77
Fringed set, family of      79
Fringed set, parametrized by a manifold      80
Fritzsche, K.      192 225 226
Fulton, W.      26 27 46 48 51 149
Fundamental group, and connectivity theorems      27
Gafmey, T.      26 27
Gauss map, definition of      44
Generalized tangent space, definition of      44
Geometric lattice and Moebius function      252
Geometric lattice, definition of      251
Gerstner, O.      154
Gibson      43
Ginsberg, V.      224
Goldstein, N.      149
Golubitsky      38 39 51
Goresky      33 37—38 46 66 117 132 147 150 153 164 167 208—222 250
Grauert, H.      52 180 225 226
Griffiths, P.      149 225 226
Grothendteck, A.      153 154 177 185
Group, Morse      211 212
Guillemin, V.      38 39 51
Haefiiger, A.      34 51
Halflink and complement of affine space      236
Halflink and complex link      66 165
Halflink and link      67 96
Halflink and normal Morse data      67 98
Halflink and quarterlink      135
Halflink of two functions      128
Halflink, definition of      66
Halflink, finitdv many possibilities      67 27
Halflink, independent of choices      67 93
Halflink, non proper      121
Halflink, relative      116
Halflink, relative nonproper      125
Hamm's theorem      185 188 200
Hamm, H.      22 148 152—164 170 185 188 200 201
Handle      73
Handlebody      21
Hansen, H.      26 27 149
Hard Lefschetz theorem      29
Hardt, R.      37 43
Hartshorne, R.      226
Henry, H.P.      45 160
hessian      5 15
Hessian and Levi form      190
Hironaka, H.      37 43 45 56 170 231
Hodge, W      29
Hoermander, L.      17
Holonomic $\mathscr{D}$ -module      223
Homotopy dimension      25
Homotopy dimension of affine varieties      25 152
Homotopy dimension of codefective pair      228
Homotopy dimension of nonproper varieties      154 200
Homotopy dimension, counterexamples      230
Homotopy dimension, local      157 205
Homotopy dimension, of a Stein manifold      15
Homotopy dimension, relative      198
Homotopy excision theorem      178
Homotopy Morse data of complex varieties      173
Homotopy Morse data, definition of      62 122
Homotopy normal Morse data      122
Hopf index theorem      21
Hopf, H.      21
Horizontal part, of link      132
IH      see “intersection homology”
INDEX      267
Intersection homology and codefective pairs      229
Intersection homology and Lefschetz theorem      26 153 217
Intersection homology and local Lefschetz theorem      156 218
Intersection homology and Morse inequalities      214
Intersection homology and Morse theory      18 147 208
Intersection homology and nonproper varieties      188
Intersection homology of complex link      214
Intersection homology of link      216
Intersection homology of Stein space      216
Intersection homology, basic properties      209
Intersection homology, specialization of      222
Intersection homology, vanishing theorems      152 216
Isotopy lemma      41
Isotopy lemma and moving the wall      71
Jet space      35 51
Johnson, F.      33 37
Johnson, K.      26
Jouanolou, J.P.      26
Karchyauskas, K.K.      22 148 152
Kashiwara, M.      212 223 224
Kato, M.      38 152 154 161 170
Kaup, L.      152 154 157 159 188 212 216 217 226 227 229
King, H.      66
Kleiman transversality theorem      39
Kleiman, S.      39 51
Koopman      33
Kunneth theorem, for intersection homology      209
Lamotke, K.      29
Lazarsfeld, R.      26 27 149
Lazzeri, F.      13 52
Le, D.T.      22 45 134 136 152—165 170 185—188 213
Lefschetz theorem and intersection homology      26 153 217
Lefschetz theorem for defective pairs      227
Lefschetz theorem with singularities      153 199
Lefschetz theorem, classical      23
Lefschetz theorem, counterexamples      230
Lefschetz theorem, for affine varieties      154
Lefschetz theorem, hard      29
Lefschetz theorem, local      26 154 202 218
Lefschetz theorem, relative      25 150 195
Lefschetz, S.      20 23 28 29 33 151 153
Levi form and Lefschetz theorem      25
Levi form and Morse index      190
Levi form of a composition      191
Levi form of distance function      193 195
Levi form, definition of      190
Levi form, restricted      192
Levi, E.E.      25 190
Levine, H.      34
Link and complement of affine spaces      246
Link and halflink      67 96
Link, connectivity of      185
Link, definition of      7 41
Link, homotopy dimension of      188
Link, horizontal part      132 162
Link, intersection homology of      216
Link, vertical part      132 162
Littlelink      142
Local calculation, of intersection homology      209
Local complete intersection and connectivity theorems      27
Local complete intersection and Lefschetz theorem      24 153
Local complete intersection and local Lefschetz theorem      156
Local complete intersection, complex link of      187
Local complete intersection, morphism      154 200 229
Local contribution, example of      256
Local Euler obstruction      161
Local homotopy dimension      157 205
Local Lefschetz theorem      26 154 202 218

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