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Harris B. — Iterated Integrals and Cycles on Algebraic Manifolds
Harris B. — Iterated Integrals and Cycles on Algebraic Manifolds



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Название: Iterated Integrals and Cycles on Algebraic Manifolds

Автор: Harris B.

Аннотация:

This subject has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen’s constructions to algebraic geometry, showing how this leads to some results on algebraic cycles and the Abel–Jacobi homomorphism. Finally, he presents a more general point of view relating Chen’s integrals to a generalization of the concept of linking numbers, and ends up with a new invariant of homology classes in a projective algebraic manifold. The book is based on a course given by the author at the Nankai Institute of Mathematics in the fall of 2001.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 120

Добавлена в каталог: 19.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^1$ current (and $L^1$ form)      72
Abel — Jacobi map      42
Algebraic equivalence of cycles      52
Angular current      82
Angular form      76 80—83 88
Archimedean height pairing      91
Asymptotic expansion      78 82
Chen's connection      7 16
Chen's Lie algebra      14
Coexact forms      16 34
Completion (inverse limit)      12 14
Current      67
CYCLE      78 84
d, $d^c$ lemma      34
Descending central series      19
Diagonal homomorphism      9 11
Dirac current      67
Euclidean heat kernel      76
Fermat quartic curve      54
First Chern form      69
Free Lie algebra      9
Green's currents      93
Green's forms      91
Group homology      22
Group-like element      11
Harmonic forms      30
Harmonic volume      42
Heat equation      75
Heat kernel      74
Heat operator      73 74
Hodge *-operator      29
Hodge theory      28
Hopf algebra      10 11
Hyperelliptic Riemann surfaces      50
Integration over the fiber      99
Intermediate Jacobian      46
Iterated integral      1
Jacobian manifold      45
Jacobian variety      45
Kahler manifold      32
Kahler metric      34
Laplace operator      30
Lattice (discrete cocompact) subgroup      26
Linking number      73 76 84—86 89
Lower central series      7
Maurer — Cartan 1-form      3
Modular curve      54
Orientations      95
Period matrix      60
Poincare — Lelong formula      69
Primitive element (of Kahler manifold Cohomology)      46
Primitive elements (in a Hopf algebra)      11
Quadratic differentials      48
Quillen homomorphism Q      8 20 21
Regularity theorem      70
Schiffer variation      47
Spherical homology classes      23
Torelli space      47
Universal enveloping algebra      8—10
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