Friedlander E.M. (ed.), Grayson D.R. (ed.) — Handbook of K-Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Friedlander E.M. (ed.), Grayson D.R. (ed.) — Handbook of K-Theory

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Название: Handbook of K-Theory

Авторы: Friedlander E.M. (ed.), Grayson D.R. (ed.)

Аннотация:

This handbook offers a compilation of techniques and results in K-theory.

These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. The overall intent of this handbook is to offer the interested reader an exposition of our current state of knowledge as well as an implicit blueprint for future research. This handbook should be especially useful for students wishing to obtain an overview of K-theory and for mathematicians interested in pursuing challenges in this rapidly expanding field.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 556

Добавлена в каталог: 30.06.2008

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Предметный указатель

with supports      254
-chain      246
-eta-invariant      730
-Rho-invariant      730
      560
      140 148 169
$w_i^{(l)}(F)$       147
$\bar{A}$ -genus, higher      762
$\bar{\mathcal{A}}$ -class      762
$\delta$ -functor      1060—1065
$\gamma$ -filtration      41
$\gamma$ -operations on K0      258
$\Gamma$ -spaces      6
$\lambda$ -operations on K0      258
$\mathbb{S}^1$       49
$\mathcal{A}$ -filtered      24
$\mathcal{F}$ -equivalence      73 82
$\Omega A$       685
$\varepsilon\mathcal{A}$       682
+-construction      see “Plus construction”
A-regular      781
A-theory      597—599
Abel’s five term relation      301
Adams operations      280
Adams spectral sequence      970
Additive category      11
Additivity theorem      22
Admissible epimorphism      11
Admissible monomorphism      11
AF algebra      849
Alexander polynomial      590
Alexander trick      711
Algebraic cycle      41
Algebraic equivalence      878 883
Algebraic K-theory of commutative Banach algebra      854
Algebraic K-theory of rings of integers      140
Algebraic K-theory of spaces      597—599
Algebraic K-theory of the integers      127 141
Algebraic n-simplex      440
Amenable group action      777
Analytic torsion      590
Approximation Lemma      75
Arakelov motivic complex      312
Artin — Verdier duality      980
Artin’s      751
Aspherical      722
assembly      30
Assembly map      735
Assembly map, analytic      804
Assembly map, relative      741
Asymptotic covering      33
Asymptotic dimension      778
Asymptotic morphism      666
Atiyah — Conjecture for Torsion Free Groups      729
Atiyah — Conjecture for Torsion Free Groups, strong      729
Atiyah — Hirzebruch spectral sequence      43 211 457 1082
Atiyah’s Real K-theory      892
Augmented diagrams      1025—1027
Augmented diagrams, constructing them      1045—1048
B      686
Balanced product of C-spaces      795
Balanced smash product of pointed C-spaces      795
Banach algebra, commutative      846
Banach algebra, semisimple      847
Bar construction      494
Based L-groups      619
Bass conjecture      386
Bass Conjecture, Strong Bass Conjecture for $K_0(\mathbb{C}G)$       753
Bass Conjecture, Strong Bass Conjecture for $K_0(\mathbb{Z}G)$       753
Bass Conjecture, Weak Bass Conjecture      754
Bass — Heller — Swan-decomposition      716
Baum — Connes conjecture      673
Baum — Connes Conjecture for Torsion Free Groups      724
Baum — Connes Conjecture with coefficients      765
Baum — Connes Conjecture with coefficients and a-T-menable groups      773
Baum — Connes Conjecture, fibered version      771
Baum — Connes Conjecture, real version      726
Baum — Connes Conjecture, status of      775
Baum — Connes Conjecture, status of the Coarse Baum — Connes Conjecture      779
BDF      see “Brown — Douglas — Fillmore theory”
Beilinson conjecture      396
Beilinson — Lichtenbaum conjecture      202 377 433 439 449 916 1101
Beilinson — Parshin conjecture      396
Beilinson — Soule conjecture      363
Beilinson — Soule vanishing conjectures      491
Bernoulli numbers      144 151 180 184 998 1002
Bicartesian square      1042
Birch — Tate conjecture      152 170
Bivariant Chern characters      694
Bivariant periodic cyclic homology      689
Bloch complex      1082
Bloch — Beilinson — Murre filtration conjecture      370
Bloch — Kato conjecture      126 202 377 449 1100 1108
Bloch — Ogus cohomology      453
Bloch — Ogus cohomology, de Rham cohomology      455
Bloch — Ogus cohomology, Deligne cohomology      455
Bloch — Ogus cohomology, etale cohomology      455
Bloch — Suslin complex      437
Bloch — Wigner function      301
Bloch’s cycle algebra      492 493
Bloch’s cycle complex      307 441
Bloch’s cycle Lie algebra      493
Bloch’s formula      276
Bloch’s formula, singular varieties      284
Blow-up      1087
Blow-up formula      201 206
Bokstedt’s JK-construction      1003
Borel class      320
Borel conjecture      722
Borel regulator      321
Bost conjecture      765
Bott element      149 169 857
Bott element, inverse      857
Bott manifold      761
Bott map      120 149
Bott periodic K-theory      125
Bott periodicity      114 117 659 846
Bott Periodicity Theorem      851
Bounded geometry      767
Bounded h-Cobordism Theorem      714
Bounded K-theory      27
Bounded map      713
Brauer group      145
Brauer lift      1003
Bredon homology      740
Brown — Comenetz duality      973
Brown — Douglas — Fillmore theory      847
Brown — Gersten spectral sequence      210
Burnside ring      816
C*-algebra      845
C*-algebra, AF      849
C*-algebra, G-C*-algebra      804
C*-algebra, maximalcomplexgroupC*-algebra      763
C*-algebra, nuclear      849
C*-algebra, reduced complex group C*-algebra      725
C*-algebra, reduced real group C*-algebra      726
C*-algebra, stable      849 859
C*-algebra, tensor product      849 860
C*-theoretic Novikov conjecture and groups of finite asymptotic dimension      778
c-equi(X, 0)      1086
Calculus of functors      72
Calkin algebra      846 858
Cancellation theorem      52 53
Categories with squares      1020—1023
Category of compactly generated spaces      794
Category of weak equivalences      16
Category with cofibrations      16
Category with cofibrations and weak equivalences      597
Category with duality      540
Category with duality, exact category with duality      543

Category with duality, triangulated category with duality      559
cdga      492
cdga, Adams graded      493
cdga, connected      493
cdga, motivic      493
cdh topology      1086
centralizer      816
Chapman — Ferry Theorem      592
Chapman’s theorem      588
Characteristic classes      583
Characteristic classes, secondary      584
Chern character      42
Chern character in algebraic geometry      361
Chern character in topology      355
Chern class      42 153 155 583 586
Chern class, coefficients in Milnor K-theory      265
Chern — Connes character      695
Chern — Simons class      584
Chern — Weil theory      583
Chow groups      1082
Chow groups, graded by (co-)dimension      247
Chow groups, higher      59
Chow groups, singular surfaces      287
Chow groups, ungraded      246
Chow ring      41
Chow’s Moving Lemma      250
Class group      143 977
Class group, ray      174
Classical polylogarithms      302
Classification of nuclear C* algebras      676
Classification of quadratic forms      556
Classifying map      681
Classifying space for a family      739
Classifying space for proper G-actions      739
Classifying space of a group      714
Classifying variety      950
Clifford algebras      118
Coarse invariance      27
Cobordism      710
Cobordism, bounded      713
Cobordism, diffeomorphic relative M-      710
Cobordism, trivial      710
Cocompact      738
Coflasque torus      944
Cohomology, continuous etale      398
Cohomology, l-adic      391
Cohomology, Lichtenbaum (Weil-etale)      404
Cohomology, motivic      361 362 371 1113
Cohomology, with compact supports      28
Commuting automorphisms      47
Completed K-theory      164
Concordance      599
Cone, reduced cone      794
Coniveau filtration      919
Connection      581
Connection, flat      582 583
Connes’ operator      88
Continuous cohomology      214
Control, bounded      591
Control, epsilon      591
Controlled K-theory      591
Correspondence      53
Correspondence, direct sum Grothendieck group      53
Cosimplicial regions      1024—1025 1068
Crystalline cohomology      91
Crystalline cycle map      206
Cubical hyperresolutions      461
Curves on K(A)      106
CW-complex, finite      712
CW-complex, finitely dominated      712
CYCLE      240
Cycle classes      506
Cycle classes, regulators by      506
Cycle classes, relative      506
Cycle complexes      440—442
Cycle complexes and Milnor K-theory      446
Cycle complexes, Chern character isomorphism      445
Cycle complexes, cubical version      450
Cycle complexes, cubical version, alternating complexes      452
Cycle complexes, cubical version, comparison with simplicial version      451
Cycle complexes, cubical version, products      452
Cycle complexes, cycle complex associated to a cycle module      262
Cycle complexes, functoriality      443
Cycle complexes, homotopy      443
Cycle complexes, localization      443
Cycle complexes, Mayer — Vietoris      443
Cycle complexes, products      444
Cycle complexes, projective bundle formula      445
Cycle complexes, properties      442
Cycle map      202
Cycle module      262
Cycle module with ring structure      262
Cycle module, cycle complex      262
Cycle, associated to a module      242
Cycle, degenerate      803
Cycle, equivalent      803
Cycle, even      803
Cycle, homotopic      803
Cycle, odd      803
Cycle, prime cycle      241
Cyclic bar-construction      78 86 101
Cyclic bicomplex      687
Cyclic homology      72 87 687
Cyclic polytopes      87
Cyclotomic tower      976
Cyclotomic trace      72 599
Cyclotomic trace map      217
Cylinder functor      19
de Rham — Witt complex      73 91
de Rham — Witt complex of a polynomial algebra      92
de Rham—Witt complex      204
Decoration      719
Dedekind zeta function      998
Deformation to the normal cone      288
Degree of a map      581 597
Deligne’s complex      307
Derived categories      1017—1018
Descent homomorphism      805
Determinant, Kadison — Fuglede      591
Devissage      1065—1067
Diffotopic      679
Dilogarithm      301 437
Dimension group      850
Dimension, birational invariance      242
Dimension, relative to a base      242
Dirac element      805
Dirac element, dual      805
Dirac-dual Dirac method      805
Disjoint union axiom      740
Distinguished polynomial      961
Distinguished triangles      1018 1035—1036
Divisor, Cartier      243
Divisor, Cartier, cap product by      245
Divisor, Weil      241
Dominated      579
Dominated epsilon      592
Duality theorem      1098
Dualizable object      972
e-invariant      147 159 164
e-Theory      661
Edge-wise subdivision      83
Eilenberg swindle      858
Eilenberg — MacLane spaces      5
Elementary module      961
Elementary spectrum      974
Elliptic operator, generalized elliptic G-operator      802
Embedding conjecture      729
Embedding theorem      487
Envelope      288
Equivalence of categories      796

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