Amorόs J., Burger M., Corlette K. — Fundamental Groups of Compact Kahler Manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Amorόs J., Burger M., Corlette K. — Fundamental Groups of Compact Kahler Manifolds

Amor&#972s J., Burger M., Corlette K. — Fundamental Groups of Compact Kahler Manifolds

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Название: Fundamental Groups of Compact Kahler Manifolds

Авторы: Amorόs J., Burger M., Corlette K.

Аннотация:

Deals with the fundamental groups of compact Kahler manifolds, collecting results from the last few years characterizing those infinite groups which can arise as fundamental groups of compact Kahler manifolds. Most of the results are negative ones, proved using Hodhe theory and its combinations with rational homotopy theory, L2 cohomology, the theory of harmonic maps, and gauge theory. Of interest to researchers and graduate students in algebraic geometry, topology, and complex analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 140

Добавлена в каталог: 02.02.2010

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Предметный указатель

${dd}^{c}$ lemma      33 131
${L}^{2}$ -cohomology      8 47—63
${L}^{2}$ -cohomology, exact      48
${L}^{2}$ -cohomology, reduced      48
1-formal space      34 36—37
1-minimal model      29—32 37 41
Albanese, dimension      23
Albanese, image      23 40—43
Albanese, map      3 22—25 40—43
Albanese, variety      22—23 41
Betti moduli space      92—94
Bochner formula      see “Siu — Sampson theorem”
Bounded geometry      48 50 53—63
Castelnuovo — de Franchis      2—3 24—25 28 43 61 63 90
Cheeger — Chern — Simons classes      106
Commutative differential graded algebra (CDGA)      30—32 35—37
Commutative differential graded algebra (CDGA), dual Lie algebra of      32
Commutative differential graded algebra (CDGA), quasi-isomorphism of      30
Commutative differential graded algebra (CDGA), weak equivalence of      30 32
Compact complex surface      4—5 10—16 25 28
de Rham fundamental group      29—46 123
de Rham fundamental group, 2-step nilpotent      38
Eilenberg — Mac Lane space      2—3 8 13 21 23 33—34 82—83
Ends of groups      8—9 12—13 47—51 60—61
Factorisation theorem      26 82—84 89—90 112
Formality      29 32—34 104—105
Formality, 1-formal space      34 36—37
Group algebra      124—125
Group completion      121—128
Group completion, $\cal P$ -completion      121
Group completion, k-unipotent      see “Pro-unipotent”
Group completion, nilpotent      122 124—128
Group completion, pro-finite      7 118 122
Group completion, pro-unipotent      9 29—46 123—128
Group completion, torsion-free nilpotent      9 43 124—128
Group, (pure) braid      8 61
Group, 1-relator      39
Group, abelian      9 116 123—125
Group, fibered      27 43 86
Group, finite      6
Group, free      7 9 11 13 16 18 27 38 49 123
Group, free product      8 11—14 47 49 109—110
Group, Heisenberg      8 39—40 49 114
Group, Higman      7 14 85—87 110
Group, lattice      see “Lattice”
Group, nilpotent      9 114
Group, non-fibered      27 43—45
Group, non-Hopfian      110

Group, non-linear      85—87 110 115—119
Group, non-residually finite      7 14 109—110 115—119
Hard Lefschetz theorem      8 38 130
Harmonic flat bundle      91—107
Harmonic flat bundle, deformation theory of      104—105
Harmonic map      9—10 26 65—90
Harmonic map, equivariant      67—69 82 92
Harmonic map, existence of      66 68 89
Harmonic map, factorisation of      26 82 89—90
Harmonic map, uniqueness of      66
Hermitian sectional curvature      71—76
Hermitian symmetric space      78—81 85
Higgs bundle      91—105
Higgs — Hermitian — Yang — Mills (HHYM) equation      97—103
Hodge signature theorem      73
Hodge structure      81 91 129—130
Hodge structure, mixed      37 45—46
Hodge structure, variation of      94—95 107
Holomorphic foliation      24 54—63 83—84 90
Hyperbolic manifold      8 13—14 77—78 82—85
Hyperkaehler manifold      100—103
Isoperimetric inequality      50—51
Lattice      7 81—83 85 87 95—96 110—111 115—119
Lefschetz hyperplane theorem      5—6 11 111—113 118
Lie algebra      76—81
Lie algebra, deformation of      104
Lie algebra, differential graded (DGLA)      104—105
Lie algebra, dual of CDGA      32
Lie algebra, lower central series of      34
Lie algebra, quadratically presented      34 36
Malcev algebra      29 34—40 125
Malcev algebra, n-step nilpotent      38 126
Malcev algebra, quadratic presentation of      34—38
Massey product      8 38—40
Normal variety      9—10
Open problem      4 7 9 85 116
Period domain      81 95
Pluriharmonic map      10 71—90
Pluriharmonic map, equivariant      72 93
Quasi-isomorphism, of CDGAs      30
Quasi-isomorphism, of DGLAs      104—105
Siu rigidity theorem      80
Siu — Beauville theorem      2—3 8 25—28 43
Siu — Sampson theorem      71—76 89 92—93 96 107
Symplectic, form      3 5 18
Symplectic, manifold      5 15—20 81
Symplectic, structure      3 5 16 18
Symplectic, sum      17—18

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