書誌事項

Index theory

Michael Atiyah

(Oxford science publications, . Collected works / Michael Atiyah ; v. 3-4)

Clarendon Press , Oxford University Press, 1988, c1987

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内容説明・目次

巻冊次

1 ISBN 9780198532774

内容説明

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. Volumes III and IV cover papers written in 1963-84 and are the result of a long collaboration with I. M. Singer on the Index Theory of elliptic operators.

目次

  • 56. The index of elliptical operators on compact manifolds.
  • 57. The index problem for manifolds with boundary.
  • 58. The index theorem for manifolds with boundary.
  • 59. Algebraic topology and elliptical operators.
  • 60. Global aspects of the theory of elliptical differential operators.
  • 61. A Lefschetz fixed-point formula for elliptical differential operators.
  • 62. A Lefschetz fixed-point formula for elliptical complexes I.
  • 63. A Lefschetz fixed-point formula for elliptical complexes II.
  • 64. The index of elliptical operators I
  • 65. The index of elliptical operators II
  • 66. The index of elliptical operators III
  • 67. The index of elliptical operators IV
  • 68. The index of elliptical operators V
  • 69. Global theory of elliptical operators.
  • 70. Index theory for skew-adjoint Fredholm operators.
  • 71. The signature of fibre bundles.
  • 72. Topology of elliptical operators.
  • 73. Resolution of singularities and division of distributions.
  • 74. Spin-manifolds and group actions.
  • 75. Riemann surfaces and spin structures.
  • 76. Vector bundles of projective 3-space.
  • 77. The index of elliptical operators.
  • 78. Elliptical operators and compact groups.
巻冊次

2 ISBN 9780198532781

内容説明

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. Volumes III and IV cover papers written in 1963-84 and are the result of a long collaboration with I. M. Singer on the Index Theory of elliptic operators.

目次

  • 79. On the heat equation and the index theorem
  • 79.a . Errata to the paper: On the heat equation and the index theorem
  • 80. Spectral asymmetry and Riemannian geometry
  • 81. Spectral asymmetry and Riemannian geometry I
  • 82. Spectral asymmetry and Riemannian geometry II
  • 83. Spectral asymmetry and Riemannian geometry III
  • 84. Hyperbolic differential equations and algebraic geometry.
  • 85. Lacunas for hyperbolic differential operators with constant coefficients I
  • 86. Lacunas for hyperbolic differential operators with constant coefficients II.
  • 87. Eigenvalues and Riemannian geometry.
  • 88. Classical groups and classical differential operators on manifolds.
  • 89. Elliptic operators, discrete groups and von Neumann algebras.
  • 90. A geometric construction of the discrete series for the semi-simple Lie groups.
  • 90.a. Erratum to A geometric construction of the discrete series for the semi-simple Lie groups
  • 91. Characters of semi-simple Lie groups.
  • 92. Geometry and analysis of Shimizu L-functions.
  • 93. Eta invariants, signature defects of cusps and values of L-functions.
  • 93. a. Signature defects of cusps and values of L-functions: the nonsplit case

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