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 Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems.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

Equivariant K-theory      122
Equivariant KK-and E-theory      667
Equivariant mapping space      80
Eta-invariant      730 861
Etale K-theory      213 978 1082
Etale K-theory for fields      125
Euler characteristic      598
Euler class      583
Exact category      11
Exact functor of categories with cofibrations and weak equivalences      16
Excision      27 33
Excision for       846
Excision for       849
Excision for algebraic K-theory      857 861—862
Excision for mod pK-theory      862
Excision for topological K-theory      857
Exotic sphere      712
Ext      660
Extension Axiom      20
Extension of length n      681
Factorial algebraic group      948
Family of subgroups      738
Farrell — Jones Conjecture and subgroups of Lie groups      780
Farrell — Jones Conjecture for $K_0(\mathbb{Q}G)$       750
Farrell — Jones Conjecture for $K_n(\mathbb{Z}G)$ for $n \leq -1$       749
Farrell — Jones Conjecture for low dimensional K-theory and torsion free groups      708
Farrell — Jones Conjecture for pseudoisotopies of aspherical spaces      769
Farrell — Jones Conjecture for torsion free groups and K-theory      714
Farrell — Jones Conjecture for torsion free groups and L-theory      719
Farrell — Jones Conjecture with coefficients      766
Farrell — Jones Conjecture, fibered version      771
Farrell — Jones Conjecture, implies the Borel Conjecture      723
Farrell — Jones Conjecture, status of the Farrell — Jones Conjecture for torsionfree groups      781
Farrell — Jones Conjecture, status of the fibered Farrell — Jones Conjecture      779
Farrell — Jones Conjecture, vanishing of low dimensional K-theory for torsionfree groups and integral coefficients      710
Fermat’s Last Theorem      144
Fiber functor      455
Field, 2-regular      177
Field, exceptional      148 165
Field, non-exceptional      148 154
Filtration of a space      46
Filtration, $\gamma$ -      258
Filtration, Brown      268
Filtration, Brown, multiplicativity of      275
Filtration, codimension of supports      256
Filtration, coniveau      256
Filtration, coniveau, multiplicativity conjecture      257 259 277 281
Filtration, coniveau, on cohomology of presheaf of spectra      269
Filtration, hypercohomology      268
Filtration, weight filtration on K-cohomology      285
Filtrations, $\gamma$ and coniveau compared      281
Finite correspondences      483
Finite correspondences, the category of      483
Finite fields      148
Finiteness obstruction      712
Fit set of primes      975
Flasque      25
Frechet algebra      861 862
Fredholm index      846
Fredholm module      861 863
Fredholm operator      121 846
Free L-groups      619
Freeness defect      962 984
Friedlander — Suslin cohomology      447
Friedlander — Suslin cohomology, comparison with higher Chow groups      447
Functional equations for the trilogarithm      303
Fundamental Theorem of Algebraic K-Theory      716
Fundamental Theorem of Hermitian K-Theory      132
Fundamental Theorem of K-Theory      868
G-CW-complex      79 738
G-CW-complex, finite      738
G-CW-complex, proper      739
G-morphism      928
G-spectra      77
G-stable category      77
G-variety      928
G-vector bundle on X      928
Gelfand transform      846
Generalized cross-ratio      324
Generalized cross-ratio of 6 points in       303
Generalized cycle map      912
Gersten complex      273
Gersten conjecture      276 279 1142
Gersten conjecture for Witt groups      567 569
Gersten conjecture, cycle complexes      264
Gersten resolution      199 201 205 211
Goncharov’s complexes      438
Goodwillie’s Theorem      862
Grassmannian polylogarithms      315
Greenberg conjecture      994 996
Gromov — Lawson — Rosenberg Conjecture, Homological Gromov — Lawson — Rosenberg Conjecture      762
Gromov — Lawson — Rosenberg Conjecture, Stable Gromov — Lawson — Rosenberg Conjecture      761
Gross conjecture      974 991 996
Gross — Sinnott kernel      983
Grothendieck group, direct sum      49
Grothendieck — Knebusch Conjecture for Witt groups      567
Grothendieck — Riemann — Rochtheorem      41
Grothendieck — Witt group      557
Group action      592 594
Group action, locally linear      595
Group, a-T-menable      774
Group, having property (RD)      776
Group, having property (T)      774
Group, having the Haagerup property      774
Group, K-amenable      764
Group, linear      777
Group, virtually cyclic      738
Group, virtually cyclic of the first kind      738
Group, virtually poly-cyclic      751
h-cobordism      588 615 624 640 710
h-cobordism theorem      588
h-cobordism, bounded      713
H-spaces      1056
H-unital      861
Handle decomposition, equivariant      595
Harris — Segal summand      149 153 159 181
Hattori — Stallings-rank      753
Heart      1049—1050
Hecke algebra      773
Hecke algebra, isomorphism conjecture for the Hecke algebra      773
Henselian pair      856
Hensel’s Lemma      856
Hermitian forms      617
Hermitian K-theory      129
Hermitian K-theory of the integers      134
Hermitian K-Theory Theorem      615
Higher Chow group sheaves      142
Higher Chow groups      196 433 440—442
Higher Chow groups, Arakelov Chow groups      312
Higher Chow groups, comparison with Friedlander — Suslin cohomology      447
Higher Chow groups, cycle classes for      508
Higher Chow groups, relative      508
Higher Hermitian K-theory      625
hilbert      90 116
Hochschild homology      74
Hodge conjecture      918
Hodge Conjecture, generalized      919
Hodge filtration      919
Homogeneous variety      936
Homology sphere      582
Homology theory, equivariant G-homology theory      791
Homology theory, G-homology theory      739
Homology theory, proper G-homology theory      791
Homotopy category of schemes      1126
Homotopy cofiber      62
Homotopy colimit problem      626
Homotopy coniveau filtration      64
Homotopy equivalence, controlled      592
Homotopy equivalence, simple      587 593
Homotopy fiber      59

Homotopy fixed point space      32
Homotopy Fixed Spectrum      625
Homotopy groups of Diff(M)      724
Homotopy groups of Top(M)      724
Homotopy invariance of $\tau^{(2)}(M)$ and $\rho^{(2)}(M)$       730
Homotopy invariance of the -Rho-invariant for torsionfree groups      730
Homotopy limit problem      626
Homotopy Orbit Spectrum      625
Homotopy-theoretic group completion      884
Homotopy-theoretic isomorphism conjecture for (G, E, F)      800
Hyper-cohomology spectrum      213
Hyperbolic functor      130 618
Hyperbolic space, H(M)      542
Hypercohomology spectrum      986 1007
Hyperenvelope      289
Idempotent conjecture      728
Igusa Stability Theorem      615
Index theorems      670
Index, secondary      861
Induction of equivariant spaces      791
Induction structure      791
Infinite loop space machine      6
Infinite loop spaces      1055—1057
Injectivity of the Baum-Connes assembly map      777
Integral $K_0(\matnbb{Z}G)$ -to- $K_0(\matnbb{Z}G)$ -conjecture      756
Integral operator, singular      844
Intersection product, commutativity for Cartier divisors      261
Intersection, multiplicity      250
Intersection, multiplicity, positivity conjecture      254
Intersection, multiplicity, Serre’s tor formula      253
Intersection, multiplicity, vanishing conjecture      254
Intersection, proper      249
Invertible spectrum      973
Irregular prime      144 145 180 182 183
Isometry      541
Isomorphism conjecture for NK-groups      772
Isomorphism conjecture for the Hecke-algebra      773
Iwasawa algebra      960
Iwasawa module      162
Iwasawa’ $\mu$ -invariant      993
Iwasawa’s Main Conjecture      995
K (compact operators)      661
K (smooth compact operators)      679
K- and L-theory Spectra over Groupoids      798
K-and L-theoretic Novikov conjecture and groups of finite asymptotic dimension      785
K-groups with coefficients      209
K-groups, algebraic K-groups of a ring      708
K-groups, negative      851 868
K-groups, reduced algebraic K-groups of a ring      709
K-groups, relative      860
K-groups, topological K-groups of a C*-algebra      725
K-groups, topological K-homology groups of a space      725
K-homology      660
K-regularity      865—868
K-theory mod n      124
K-theory of $\mathbb{Z}/p^n\mathbb{Z}$       107
K-theory of algebraically closed fields      124
K-theory of Number Fields      143
K-theory of Quadratic Forms      617
K-theory of stable C*-algebras      129
K-theory spectrum      121
K-theory spectrum of an exact category      270
K-theory spectrum over groupoids      798
K-theory spectrum, algebraic      851
K-theory spectrum, algebraic K-theory spectrum of a ring      714
K-theory spectrum, modn      853
K-theory spectrum, topological      851
K-theory spectrum, topological, connective      855
K-theory, negative      591
K-theory, product on      271
K-theory, Volodin      862
Kadison Conjecture      728
Kahnmap      153 155 161
Kaplansky conjecture      729
Karoubi Conjecture      859 862—865
Karoubi Conjecture, unstable      865
Karoubi Periodicity      619 628 632
Karoubi’s forgetful trick      629
Karoubi’s hyperbolic trick      630
Kasparov module      662
Kasparov product      804
Kato Conjecture      415
Kimura — O’Sullivan Conjecture      412
KK-theory      661
KK-theory, equivariant      804
Knot      590
Kobal’s Forgetful Theorem      629
Kobal’s Hyperbolic Theorem      630
KR-theory      121
Kummer — Vandiver Conjecture      999
L theory spectrum      637
l-adic completion      966
l-adicL-function      993
L-class      732
L-groups      719
L-theory of Quadratic Forms      619
L-theory spectrum over groupoids      798
L-theory spectrum, algebraic L-theory spectrum of a ring      719
Lagrangian      544 559
Laurent series      121
Lawson homology      896
Layer of a filtration      46
length function      775
Lens space      590
Leopoldt Conjecture      991 996
Leopoldt defect      980 985
Lichtenbaum conjecture      393 397
Lichtenbaum-Quillen Conjecture      125 215 358 986
Lichtenbaum-Quillen Conjecture forZ      999
Lichtenbaum-Quillen Conjecture, 2-adic      1004 1006
Lichtenbaum-Quillen Conjecture, generalized      996
Lie groups, made discrete      854
Liftable simplices      1049
Linear varieties      914
Linearization map      597
Local cyclic cohomology      692
Local cyclic homology      693
Local fields      150 980
Localisation      1013 1057—1059
localization      198 210 1087
Localization theorem      19
Locally convex algebra      679
Locally finite homology      29
Logarithmic de Rham — Witt sheaf      205
Long exact sequence in KK      664
Lower K-groups      23
Lower L-groups      620
m-algebra      679
Main Conjecture of Iwasawa Theory      157 170
Manifold parametrized over $\mathbb{R}^k$       713
Manifold structure      621 639
Manifold, parallelizable      583
Mapping cylinder neighborhood      595
Mayer — Vietoris      1087
Merkurjev — Suslin conjecture      365
Meta-Conjecture      735
Metabolic symmetric space      544 559
Metrically proper      774
Milnor conjecture      1108
Milnor K-groups      356
Milnor K-theory      201 1095 1107
Milnor K-theory of a field      261
Mixed Tate motives      450 458 488
Mixed Tate motives, $K(\pi, 1)$ -conjecture      502
Mixed Tate motives, Bloch — Kriz      500
Mixed Tate motives, Bloch — Tate      494
Mixed Tate motives, Kriz — May      500
Mixed Tate motives, Spitzweck representation theorem      501 502
Mixed Tate motives, triangluated category of      489
Mixed Tate motives, triangluated category of t-structure      491

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