Rosenberg J. — Algebraic K-Theory and Its Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Rosenberg J. — Algebraic K-Theory and Its Applications

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Название: Algebraic K-Theory and Its Applications

Автор: Rosenberg J.

Аннотация:

Algebraic K-theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-theory.

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 392

Добавлена в каталог: 16.04.2005

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Предметный указатель

Reduced Hochschild complex      6.1.38
Reduced Jf-theory      13.2 1.6.2
Reduced word      6.3.15
Regular ring      3.1.2(4)
Relative CW-complex      5.1.7
Relative group, $H^\lambda$       6.1.27(2—3)
Relative group,       1—5.3
Relative group, and for categories      3.1.26
Relative group,       2.5.1
Relative group, HC      6.1.17
Relative group, HH      6.1.8
Relative group, higher K      5.2.14
Relative group, Mennicke symbols for      2.5.12
Resolution Theorem      3.1.13 3.1.14 5.3.25
Riemann — Roch theorem      3.1.17
Riemann — Roch Theorem, Grothendieck's generalized      3.1.25
Rim's Theorem      2.5.8
Ring without unit      1—5-6
Ring without unit, of      1—5.7
Rummer's theorem      4.4.17
s-cobordism theorem      2.4.4
Schur's lemma      3.1.2(5)
Section extension property      5.1.1
Serre duality theorem      remarks following 3.1.18
Shapiro's Lemma      3.1.2(4) 4.1.12
Sheaf cohomology      remarks following 3.1.16
Siebenmann's Theorem on putting a boundary on a manifold      1.7.14
Simple space      5.1.6 5.2.11—5.2.12
Skeleton      5.1.7
Smash product      5.3.1 6.3.20
Spectrum in algebraic topology      beginning of 5.1 remarks
Spectrum joint essential      4.4.20
Spectrum of a ring      remarks preceding 1.3.12
Spectrum of an operator      2.2.10 2.2.11 6.3.8
Spherical space form      1.7.15
Stable homotopy      5.2.19 remarks
Stable isomorphism of central simple algebras      4.4.13
Stable range for       remarks following 2.3.3 2.3.5
Stable range for       4.3.12
Steinberg symbol      4.2.12 4.2.17 4.3.3
Stone — Cech compactification      1.7.14
Strict unit      5.2.13
Suslin's Theorem on K-theory of $\mathbb R$ and $\mathbb C$       5.3.9
Suslin's Theorem on K-theory of algebraically closed fields      5.3.8 5.3.34
Swan's Theorem      1.6.3
Symmetric group      5.2.19
Tietze extension theorem      1.6.5 5.1.1
Toeplitz algebra      4.4.30 6.3.29

Toeplitz operator      4.4.30
Topological K-theory      1.6.2
Topological K-theory, calculation for spheres      1.6.13
Topological K-theory, classifying space for      5.3.2 5.3.9
Trace class (of operators)      2.2.10
Trace map on       6.2.4
Trace map on higher K-groups      6.2.14
Trace of an operator      2.2.10
Trace on       6.3.11
Trace on a ring      6.1.33
Trace, faithful      6.3.10
Trace, generalized      6.1.36
Trace, normalized      6.3.10
Trace, positive      6.3.10
Trace, self-adjoint      6.3.10
TRANSFER      3.2.29 4.1.21 5.3.23 5.3.40
Unitary group      1.6.13 2.4.2
Unitary operator      2.2.10 3.3.8(4)
Universal central extension      4.1.2
Universal central extension and       4.1.19
Universal central extension of icosahedral group      4.1.27
Universal central extension, characterization of      4.1.3 4.1.18
Universal coefficient theorem      4.1.13 6.1.24
Vector bundle      1.6.1
Vector bundle, hermitian metric on      1.6.3
Virtual flat G-bundle      5.3.31
Virtual flat R-bundle      5.3.33 6.2.25
Wall finiteness obstruction      1.7.12 1.7.15 1.7.19
Wall obstruction group      1.7.12
Wall obstruction group for cyclic group of prime order      3.3.5(b)
Wall obstruction group for product with $\mathbb Z$       3.3.9
Wall obstruction group for quaternion group      1.7.20
Whitehead group      2.4.1
Whitehead group for cyclic group of odd prime order      2.5.6(b) 2.5.9 2.5.15
Whitehead group for cyclic group of order 2      2.4.3
Whitehead group for cyclic group of order 3      2.5.18
Whitehead group for finite abelian group      2.5.16
Whitehead group for product with $\mathbb Z$       3.2.27
Whitehead torsion      2.4.6 2.4.9
Whitehead torsion, and classification of manifolds      2.4.4
Whitehead torsion, behavior under products      2.4.11
Whitehead's Lemma      2.1.4
Whitehead's Lemma, relative version      2.5.3
Whitehead's Theorem      5.1.13
Whitney sum      1.6.1
Zariski topology      remarks preceding 1.3.12
Zeta function      remarks preceding 5.3.14
“Eilenberg swindle”      1.1.8

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