A. du Plessis, Wall T. — The Geometry of Topological Stability (London Mathematical Society Monographs New Series) :: Электронная библиотека попечительского совета мехмата МГУ

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A. du Plessis, Wall T. — The Geometry of Topological Stability (London Mathematical Society Monographs New Series)

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Название: The Geometry of Topological Stability (London Mathematical Society Monographs New Series)

Авторы: A. du Plessis, Wall T.

Аннотация:

In presenting a detailed study of the geometry and topology of numerous classes of "generic" singularities, Geometry of Topological Stability bridges the gap between algebraic calculations and continuity arguments to detail the necessary and sufficient conditions for a C (infinity) to be C0-stable. Throughout, the authors masterfully examine this important subject using results culled from a broad range of mathematical disciplines, including geometric topology, stratification theory, algebraic geometry, and commutative algebra. Packed with original research, much of which is presented here for the first time, the book will be welcomed by students and researchers interested in singularity theory and related areas.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 584

Добавлена в каталог: 30.10.2010

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Предметный указатель

$(\ast,\ast)$ -continuous      59
$CS-\ast-C^{r}$ -stable map      102
$C^{0}$ -unstable      127
$C^{r,s}$ -foliation      366
$C^{r}$ path topology      67
$C^{r}$ -persistent      132
$C^{r}$ -stable (germ)      111
$C^{r}$ -stable (map)      95
$C^{\infty}$ -self-persistent (germ)      26
$C^{\infty}$ -stable (germ)      26
$C^{\infty}$ -stable (map)      27
$P(d)-C^{r}$ -stable (germ)      112
$P(d)-C^{r}$ -stable (map)      96 101
$P-(C^{\infty})$ -stable (germ)      26
$W-\ast-C^{r}$ -stable (map)      403
$\ast$ germ class      123
$\ast$ -immersive (jet)      170
$\ast$ -kernel      170
$\ast$ -parameter- $\ast$ -stable (germ)      112
$\ast$ -parameter- $\ast$ -stable (map)      96
$\ast$ -persistent (germ)      126
$\ast$ -product- $C^{r}$ -stable (germ)      113
$\ast$ -product- $C^{r}$ -stable (map)      98
$\ast$ -self-persistent      26 126 130
$\ast$ -transverse (germ)      123
$\ast$ -transverse (jet)      170
$\mathscr{E,K}$ -equivalence (germs)      30
$\mathscr{K}$ -finite      23
$\mathscr{K}$ -germ class      163 199
Almost stable (germ)      413
Apolar system      292
Avoidance (of germ class)      123
Basic pairing      427
Bifurcate      201
Blow-up, $\sum^{2,1}$ -series      269
Blow-up, E-series      234
Blow-up, Fe-series      290
Blow-up, G-series      216
Blow-up, I-series      257
Blow-up, W-series      218
Blow-up, Z-series      304
Canonical (stratification)      34
Cartesian diagram      24
Civilized (stratum in jet space)      345
Codimension (germ class)      123 201 263
Cone-like (representative)      44
Contact equivalence      22
Controlled vector field      35
Counting components      136
Critical (germ class)      123
Critical case ( $\sum^{2,1}$ )      274
Critical multiplicity      162
Critical point, set      20
Critical value stratification      38
Damon germ      349
Damon spectral sequence      443
Damon stratum      349
Deform, deformation      201
Discriminant      20
Discriminant matrix      421
Discriminant module      421
Disrupted on      136
Disruptive (germ)      127 136
Disruptive in off-dimensions      179
Equidimensional case      266
Equivalent number of moduli      280
Euler relation      424
Euler vector field      386
Exceptional deformations      210
Exhaustion      57
Extended stable unfolding      400
Extended tangent space      23
Extension (of map-germ)      478
Extremely tame (=E-tame) (retraction)      366
Feebly $C^{0}$ -persistent      135
Fine ST-invariant      188
Finite singularity type (germ)      29
Finite singularity type (map)      31
Finitely determined (germ)      23
Flow      34
Fold (germ, jet, map)      48
Frontier condition      38
Generally non-transverse      48 414
Generated by germ      123
Generated, germ class      123
Germ      20
Height (of germ)      202 247
Height (of partition)      296
Hilbert — Samuel function      271
Homogeneous      386
Homotopically stable (germ)      26
Immersion condition (=IC)      166
Improper point      50
Infinitesimally stable (germ)      25
Infinitesimally stable (map)      27
Instability ideal      422
Instability locus      398 402
Instability matrix      422
Instability module      422
Instability sheaf      410 411
Instability space      410 411
Integrable (field of q-planes)      371
Integrable (vector field)      36 368
Integral curve      34
Isotopy lemmas of Thom      37 39
J-extension      266

Jacobian ideal      29
Jacobian matrix      22
jet      21
Level $\delta$ , for G-series      234
Level $\gamma$ , for U-series      244
Level $\kappa$ , for $\sum^{2,1}$       269
Level $\varepsilon$ , for I-series      257
Lift (of vector field)      35
Lifted positive instability ideal      438
Linear reduction, J'-, K'-, L- and M-series      253
Linear reduction, J-, F-series      231 233
Link      165
Local algebra Q(f^) (of germ)      29
Locally $C^{\infty}$ -stable (map)      28
Locally integrable vector field      34
LST-invariant (germ class)      163 199
Mild (extension of map-germ)      482
Miniversal (unfolding)      25
Morphism (of unfoldings)      25
MT-stable (map, germ)      47
MT-type(germ)      47
Multi-A-regular      193
Multigerm      21
Multijet      21
Multiplicity (of germ)      162
Multitransverse      28
Near-IC      172
Nearby (germ classes)      126
Nice dimensions      28 264
Nondegenerate critical point      48
Normalization ( $\sum^{2,1}$ germ)      275
Poincare series      460
Positive instability ideal      422
Positive instability locus      402
Positive instability matrix      422
Positive instability module      422
Positive unfolding      400
Presentation (of germ class)      123
Proper (map)      50
Proper unfolding      24
Property $P_{Q}, P\ast_{Q}$       124
Q-disruptive in off-dimensions      179
Quadratic reduction, Q-, S-, K-series      221 223 232
Quasi-disruptive (=Q-disruptive) (germ)      153 183
Quasi-proper (map)      50 345
Real multiplicity      162 260
Real Segre symbol      297
Reduced ideal      411
Regular intersection      27 33
Regular stratification, Bekka- or C-      40
Regular stratification, Thom-      38
Regular stratification, Whitney-      32
Relative height      202
Representative (of germ)      20
Retraction of maps      357
Retraction of pairs      346 373
Semi-nice dimensions      264
Sharp neighbourhood      67
Short deformations      204
Slope, $\alpha$ , $\beta$ for E-, W-series      216 218
Smooth (map of function spaces)      72
Source      21
Source disruptive      151
Source presentation      123
Special representative (of germ)      43
Split (real form)      204
ST-distinct      178 199
ST-equivalent      163
ST-invariant      199
Stable point      398
Standard form (of unfolding)      25
Stratification (of map)      38
Stratification (of space)      32
Stratified vector field      34
Strict $P_{Q}$       126
Strict presentation (of germ class)      123
Strong $C^{\infty}$ -stability (map)      27
Strong $P_{Q}$       126
Strongly $C^{r}$ -stable (germ)      112
Strongly $C^{r}$ -stable (map)      96 101
Strongly disruptive      127
Subcritical, supercritical ( $\sum^{2,1}$ germs)      274
Suspension (of germ class)      163 199
Suspension (of germ)      30
T-strongly- $C^{r}$ -stable (map)      101
T-uniformly- $C^{r}$ -stable (map)      101
Tame retraction germs      97 346 357 360
Tame retraction maps      97 346 357 360
Tame retraction pairs      97 346 357 360
Tamely-P- $C^{0}$ -stable (germ)      113
Tamely-P- $C^{0}$ -stable (map)      97
TARGET      21
Topologically (non-) critical      124
Trivial (unfolding)      26
Unfolding      24
Unfolding monomials      399
Uniformly- $C^{r}$ -stable (germ)      112
Uniformly- $C^{r}$ -stable (map)      96 101
Unstable deformations      501
Versal (unfolding)      25
Very tame (=V-tame) (retraction)      346 361
Weak $P(Q_{0})$       126
Weak control (of vector field)      35
Weakly $C^{0}$ -persistent      135
Weakly regular (stratification)      40
Weighted norm      386
Weights, (weighted) homogeneous      386 399

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