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Ranicki A.A. — Algebraic L-theory and Topological Manifolds
Ranicki A.A. — Algebraic L-theory and Topological Manifolds

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Название: Algebraic L-theory and Topological Manifolds

Автор: Ranicki A.A.

Аннотация:

This book presents the definitive account of the applications of this algebra to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincaré duality space with a local quadratic structure in the chain homotopy type of the universal cover. The difference between the homotopy types of manifolds and Poincaré duality spaces is identified with the fibre of the algebraic L-theory assembly map, which passes from local to global quadratic duality structures on chain complexes. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one.


Язык: en

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 358

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha(F, \pi)$, $\alpha_D(F, \pi)$ simple factors in $F[\pi]$      225
$\alpha^k(F, \pi)$ F-multisignature components      232
$\Delta$-map      118
$\Delta$-map, compactly supported      119
$\Delta$-map, homotopy      118
$\Delta$-map, simplicial complexes      77
$\Delta$-set      117
$\Delta$-set, finite      119
$\Delta$-set, function      118
$\Delta$-set, geometric product      118
$\Delta$-set, Kan      118
$\Delta$-set, locally finite      117
$\Delta$-set, loop      120
$\Delta$-set, mapping fibre      120
$\Delta$-set, pointed      119
$\Delta$-set, realization      117
$\Delta$-set, spectrum      121
$\mathbb C$-contractible, chain complex      51
$\mathbb C$-contractible, quadratic complex      51
$\mathbb C$-contractible, symmetric complex      51
$\mathbb C$-equivalence      51
$\mathbb C$-Poincare quadratic complex      51
$\mathbb C$-Poincare symmetric complex      51
$\mathbb L$-spectrum, normal      138 145 173
$\mathbb L$-spectrum, quadratic      138 145 173 286
$\mathbb L$-spectrum, symmetric      134 145 173 286
$\mathbb L$-spectrum, visible symmetric, $\mathbb{VL}(R, K)$      145
(R, K)-modules      85
(R, K, w)-module      308
1/2-connective algebraic bordism categories $\Lambda\langle1/2\rangle(R, K)$, $\widehat\Lambda\langle1/2\rangle(R, K)$      164
1/2-connective normal, $\mathbb L$-spectrum $\mathbb{NL}^*\langle1/2\rangle(R)$      164
1/2-connective normal, $\mathbb L$-spectrum $\mathbb{VL}^*\langle1/2\rangle(R, K)$      165
1/2-connective normal, complex      164
1/2-connective normal, L-groups $NL^*\langle1/2\rangle(R, K)$      164
1/2-connective normal, signature      179
1/2-connective visible symmetric, L-groups $VL^*\langle1/2\rangle(R, K)$      164
Algebraic bordism category, $\Lambda(R)_*(K)$      97
Algebraic bordism category, $\Lambda(R)_*(K, w)$      308
Algebraic bordism category, $\Lambda(R, K)$      97
Algebraic bordism category, $\Lambda(R, K, w)$      309
Algebraic bordism category, $\Lambda^*(K)$      75
Algebraic bordism category, $\Lambda^q(R)\, (q=p, h, s)$      55
Algebraic bordism category, $\Lambda_*(K)$      75A (AT) 75
Algebraic bordism category, $\Lambda_+(R)$      59
Algebraic bordism category, Algebraic $\Lambda =(\mathbb A, \mathbb B, \mathbb C)$      51
Algebraic bordism category, connected      61
Algebraic bordism category, functor      53
Algebraic mapping cone      25
Algebraic normal complex      40
Algebraic surgery      33
Algebraic surgery, exact sequence      148
Algebraic surgery, twisted      316
Assembly, $\mathbb A^*(K)\to\mathbb A$      63
Assembly, $\mathbb A_*(K)\to\mathbb A$      63
Based object      63
Boundary, dual cell $\partial D(\sigma, K)$      68
Boundary, normal complex      45
Boundary, quadratic complex      34
Boundary, symmetric complex      34
Canonical fundamental class, manifold $[X]_Х\mathbb L}$      186
Canonical fundamental class, normal complex $[X]_{\mathbb{NL}}$      181
Canonical fundamental class, normal complex $[X]_{\mathbb{NL}}$, transversality structure $[Z]_\Pi$      186
Canonical orientation, spherical fibration $\widehat U_\nu$      174
Canonical orientation, topological bundle $U_{\overline \nu}$      174
Category, R-module, based f.g. free $\mathbb A^S(R)$      55
Category, R-module, f.g. free $\mathbb A(R)$      29
Category, R-module, f.g. free $\mathbb A^h(R)$      28
Category, R-module, f.g. projective $\mathbb A^p(R)$      28
Cech complex      73
Cech-deRham complex      73
Chain bundle $(C, \gamma)$      39
Chain complex category, $\mathbb B(R)$      56
Chain complex category, $\mathbb B(\mathbb A)$      26
Chain complex category, $\mathbb B_+(R)$      59
Chain complex category, $\mathbb C(R)$      56
Chain complex category, $\mathbb C(\mathbb A)$      51
Chain complex category, $\mathbb C_+(R)$      59
Chain complex, dimension      25
Chain complex, dual TC      27
Chain complex, finite      25
Chain complex, highly $\mathbb B$-connected      60
Chain complex, highly connected      60
Chain complex, homogeneous      110
Chain complex, n-dual $\Sigma^nT(C)$      27
Chain complex, pair      137
Chain complex, suspension SC      25
Chain complex, suspension SC, 0-dimensional      27
Chain duality      27
Closed subcategory      51
Cobordism, cycle      126
Cobordism, quadratic Poincare complex      32
Cobordism, symmetric Poincare complex      32
Codimension q, Poincare transversality obstruction      260
Codimension q, splitting obstruction      259
Cohomology groups, $H^*(K, w;\mathbb F)$      311
Cohomology groups, $H^*(K;\mathbb F)$      122
Cohomology spectrum, $F^{K_+}$      122
Cohomology spectrum, $F_{\mathbb Z_2}^{K_+}$      311
Combinatorial diagonal approximation      317
Compactly supported Cech-deRham complex      73
Compactly supported cohomology groups $H_c^*(K;\mathbb F)$      122
Compactly supported cohomology spectrum $\mathbb F_c^{K_+}$      122
CYCLE      125
Cycle, $\{\mathbb F\}$-cycle      131
Cycle, relative      127
Degree $d_j(F, \pi)$      225
Derived Horn      87
Derived product      86
Dissection      71
Division algebra $D_j(F, \pi)$      225
Double skew-suspension, $\overline S^2$      32
Dual cell $D(\sigma, K)$      67
Dual cell $D(\sigma, \tau)$      70
Geometric Thorn class      93
Global 1-equivalence      179
Global equivalence      97
Highly $\mathbb B$-connected quadratic complex      60
Highly $\mathbb B$-connected quadratic pair      60
Homogeneous envelope      110
Homology groups      122 131 311 313
Homology spectrum      122 131 311 313
Homotopy colimit      125
Homotopy equivalence, normal complexes      41
Homotopy equivalence, quadratic complexes      30
Homotopy equivalence, symmetric complexes      30
Homotopy invariant functor      132
Idempotent $e_j(F, \pi)$      228
Involution      27
L-groups, connective symmetric, $L^*(R)$      60
L-groups, highly $\mathbb B$-connected, $L_n(\Lambda)^{hc}$      60
L-groups, hyperquadratic, $\widehat L(\mathbb A)$      45
L-groups, normal      41 52 98 173 310
L-groups, quadratic      32 33 52 98 219 258 310
L-groups, reduced quadratic      253
L-groups, round      235
L-groups, symmetric      32 33 52 98 219 310
L-groups, visible symmetric      98 99 173 286 303 310 329
Link      67
Local equivalence      97
Locally Poincare quadratic complex      89
Locally Poincare symmetric complex      89
locally q-Poincare simplicial complex      157
locally q-Poincare symmetric complex      156
LS-groups $LS_*(\Phi)$      258
Map, algebraic normal complexes      40
Map, chain bundles      39
Map, quadratic complexes      30
Map, symmetric complexes      30
Mapping cofibre      121
Multirank $r_*(P)$      226
Multisignature K-theory      224
Multisignature L-theory      232
Nerve      71
Normal, complex, algebraic      40
Normal, complex, geometric      42
Normal, invariant, 4-periodic $[f, b]_{\overline{\mathbb L}}$      294
Normal, invariant, 4-periodic $\overline{t}(i, b)$      295
Normal, invariant, homotopy equivalence t(f)      197
Normal, invariant, normal map $[f, b]_{\mathbb L}$      196
Normal, invariant, TOP reduction t(b)      196
Normal, map, algebraic      49
Normal, pair, algebraic      40
Normal, pseudomanifold      180
Normal, structure, algebraic $(\gamma, \xi)$      40
Novikov conjecture      271
Novikov group      275
number of embeddings of field F, complex $n_{\mathbb C}(F)$      248
number of embeddings of field F, involution $n_{\mathbb C}(F, \mathbb Z_2)$      248
number of embeddings of field F, negative $n_{\mathbb R}^-(F_0, a)$      248
number of embeddings of field F, positive $n_{\mathbb R}^+(F_0, a)$      248
number of embeddings of field F, real $n_{\mathbb R}{F)$      248
Open star      68
Poincare complex, geometric      42
Poincare complex, quadratic $(C, \psi)$      30
Poincare complex, symmetric $(C, \phi)$      30
Poincare complex, topologically reducible      181
Poincare duality group      275
Poincare pair, quadratic      31
Poincare pair, symmetric      31
Poincare transverse      185
Preassembly      320
Pseudomanifold      91
q-connective, $\mathbb L$-spectrum, normal      151
q-connective, $\mathbb L$-spectrum, quadratic      151
q-connective, $\mathbb L$-spectrum, symmetric      151
q-connective, $\mathbb L$-spectrum, visible symmetric      163
q-connective, algebraic bordism category      157
q-connective, complex, chain      156
q-connective, complex, normal      156
q-connective, complex, quadratic      156
q-connective, complex, symmetric      156
q-connective, cover $\mathbb F\langle q\rangle$      151
q-connective, L-groups, $VL^*\langle q\rangle(\Lambda)$      163
q-connective, L-groups, normal      151
q-connective, L-groups, quadratic      151
q-connective, L-groups, symmetric      151
q-connective, spectrum      151
q-connective, structure groups, quadratic      158
q-connective, structure groups, symmetric      159
q-connective, structure spectrum, quadratic      159
q-connective, structure spectrum, symmetric      159
Q-groups, hyperquadratic Q*(C)      38
Q-groups, quadratic      30
Q-groups, symmetric      30
Q-groups, twisted quadratic      39
Q-groups, visible symmetric      99
Quadratic kernel      49
Rank of Witt group $r^k{D)$      231
Relative $\mathbb F$-homology      127
Resolution      283
Signature      232
Signature, 4-periodic $\overline{\sigma}^*$      292
Signature, bounded visible $\sigma^*$      329
Signature, codimension n, global      277
Signature, codimension n, local      277
Signature, codimension n, quadratic      277
Signature, codimension n, symmetric      277
Signature, higher      269
Signature, hyperquadratic $\widehat\sigma^*$      47
Signature, normal      105
Signature, normal $\widehat\sigma^*$      47
Signature, quadratic      105
Signature, quadratic $\sigma_*$      49
Signature, symmetric $\sigma^*$      47
Signature, visible symmetric      104
Signature, visible symmetric $\sigma^*$      99
Simple factor $S_j(F, \pi)$      225
Stable algebraic bordism subcategory      58
Stable closed subcategory      58
Star      67
Structure group, quadratic      148 190 263 286 315
Structure group, symmetric      149
Structure invariant s(f)      197
Structure invariant s(f), 4-periodic $\overline{s}(f)$      295
Structure set $\mathbb S^{TOP}(X)$      195
Structure set $\mathbb S^{TOP}(X)$, $\Lambda$-coefficient $\mathbb S^{\Lambda TOP}(M)$      303
Structure spectrum, quadratic      148 315
Structure spectrum, quadratic, symmetric      149
Supplement      123
Surgery exact sequence, $\Lambda$-coefficient      304
Surgery exact sequence, algebraic      169
Surgery exact sequence, geometric      195
Surgery exact sequence, q-connective algebraic      159
Suspension, (symmetric, quadratic) pair      43
Suspension, chain complex SC      25
Suspension, spectrum $\Sigma K$      121
Topological reducibility obstruction, difference element $t(\overline\nu, \overline\nu')$      175
Topological reducibility obstruction, homotopy equivalence t(f)      197
Topological reducibility obstruction, Poincare complex t(X)      181
Topological reducibility obstruction, spherical fibration $t(\nu)$      174
Total complex      25
Total surgery obstruction s(X)      190
Total surgery obstruction s(X), $\Lambda$-coefficient $s(X;\Lambda)$      303
Total surgery obstruction s(X), 4-periodic $\overline{s}(X)$      292
Total surgery obstruction s(X), bounded $s^b(K)$      329
Total surgery obstruction s(X), lower $s^{\langle -i\rangle}(X)$      325
Total surgery obstruction s(X), projective $s^p(X)$      324
Totally imaginary      248
Totally real      248
TRANSFER      215
Transversality structure      185
[R, K]-modules      85
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