Roe J. — Index Theory, Coarse Geometry and Topology of Manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Roe J. — Index Theory, Coarse Geometry and Topology of Manifolds

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Название: Index Theory, Coarse Geometry and Topology of Manifolds

Автор: Roe J.

Язык:

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 100

Добавлена в каталог: 23.11.2004

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Предметный указатель

$(\pi-\pi)$ -theorem      50 59
$C^{\ast}$ -algebra      17 72 89
$C^{\ast}$ -algebra of a coarse space      see “ $C^{\ast}(X)$ ”
$C^{\ast}$ -algebra of a group      18
$C^{\ast}$ -algebra, crossed product      33
$C^{\ast}(X)$       19
$D^{\ast}(X)$       38
$\alpha$ -approximation theorem      67 84
$\varepsilon$ -propagation      20 84
Assembly map      38—44 50 52 64 69 74 80 88
Assembly map, Baum — Connes      43 75
Assembly map, coarse      69
Assembly map, equivariant      43
Baum — Connes conjecture      34
Baum — Connes conjecture, coarse      see “Coarse Baum — Connes conjecture”
Bordism      30 31 45 49 56 63 66 67
Bordism, spin      55
Bott periodicity      25 34
Boundary of a cone-like end      58
Boundary of an operator      see “Operator”
Boundary of compactification      88
Boundary, Gromov      85
Boundary, Higson      89
Boundary, map      21 28 41 63
Bounded geometry      13 34 61 62 70 84 88
Chopping function      4 20 38
Chopping function, exact      58
Classifying space      13 31 53 71 75
Coarse Baum — Connes conjecture      70 71 80 82
Coarse Baum — Connes conjecture with coefficients      75
Coarse, homology      14—16 69
Coarse, map      9 19 32 34 39 63 80 88
Coarse, structure      10 13 40 87
Coarse, structure bounded      87
Coarse, structure continuously controlled      88
Coarsely equivalent      10
Coarsening      14 69
Coarsening sequence of covers      15
Cobordism      see “Bordism”
Compactification      88
Compactification, coarse      88
Compactification, Higson      89 92
Concordant      55 60
Descent principle      71 86 91
Dranishnikov space      70
Eilenberg swindle      79 83
Elliptic regularity      3 20
END      58
Excision      37 89
Excision, strong      80
Excisive, decomposition      77
Excisive, functor      72
Finite propagation speed      20 38
Flasque      78 81
Fredholm module      35
Functional calculus      3 20 62
Grading      4 21 28 38 62
Gromov — Lawson invariant      59
h-cobordism      45 55 65
Higher ${}^{A}$ -genus      32 44
Higher index theorem      see “Index higher”
Higher signature      32 53 66
Hilbert — Poincare space      61
Homotopy fixed set      71
Hyperbolic differential equation      20
Hyperbolic space      9 85
INDEX      4 21 29 38 58
Index theorem      6—7
Index theorem for $\mathbb{R}^n$ -bounded manifold      34 67

Index theorem for partitioned manifold      30—32 44
Index theorem, higher      8 27—34 74
Index theorem, relative      23
Index, coarse      21 34
Index, families      74
Index, relative      22
K-homology      15 28 35—38 70 89
K-theory      19 24—26
Kasparov’s lemma      36 59 83 90
Lichnerowicz theorem      6 22 55 58
Lipschitz homotopy      80—83
Lipschitz map      11 79
Mayer — Vietoris sequence      25 72
Mayer — Vietoris sequence for coarsely excisive decomposition      77
Mayer — Vietoris sequence for K-homology      37
Microlocal analysis      67
Module      3 18 58
Module, adequate      19 89
Module, covariant      41
Module, covariant, $\Gamma$ -adequate      42
Module, Fredholm      see “Fredholm module”
Module, Hilbert      75
Multiplier algebra      20 41
Noncommutative geometry      17—18
Normal invariant      47—49
Normal map      48 65
Novikov conjecture      43 51—53 66 71 83
Open cone      11 58 79 83
Operator, boundary of      27—28
Operator, compact      3 25
Operator, Dirac and assembly      40
Operator, Dirac, defines homology class      38 57
Operator, Dirac, generalized      2
Operator, Dirac, spinor      5 27
Operator, finite propagation      19 27 38 39 88
Operator, Fredholm      4
Operator, locally compact      3 18 36
Operator, pseudodifferential      36
Operator, pseudolocal      36
Operator, signature      5 27 61
Operator, supported near a set      22 59 78
Operator, unbounded      1
Partition of a manifold      29
Pimsner — Voiculescu exact sequence      33
Poincare duality      5 38 47 61 62 71 74
Pontrjagin classes      7 52
Pontrjagin classes, topological invariance      66
Positive scalar curvature      6 22 54—61
Proper action      14 41 75
Rough geometry      16 34
s-cobordism theorem      12 46
Scaleable      83
Shrinking      82
Signature      5 32 52 63 67
Signature, higher      see “ Higher signature”
Signature, Hilbert — Poincare      62
Signature, operator      see “Operator signature”
Structure algebra      43 57
Structure invariant of homotopy equivalence      64
Structure invariant of positive scalar curvature metric      58
Structure set      46 65
Surgery      6 45—56
Surgery, bounded      53 66 69
Surgery, exact sequence, analytic      43 58 72
Surgery, exact sequence, geometric      47
Surgery, exact sequence, transformation from geometric to analytic      65
Surgery, obstruction groups      49—51 54
Trace      28
Uniformly contractible      13 16 70 88
Universal cover      10 14 43 63

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