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Topological Methods in Algebraic Geometry : Classics in Mathematics - F. Hirzebruch

Topological Methods in Algebraic Geometry

Classics in Mathematics

Paperback Published: February 1995
ISBN: 9783540586630
Number Of Pages: 234

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This text examines topological methods in algebraic geometry.

Introductionp. 1
Preparatory material
Multiplicative sequencesp. 9
Sheavesp. 16
Fibre bundlesp. 37
Characteristic classesp. 49
The cobordism ring
Pontrjagin numbersp. 76
The ring [actual symbol not reproducible]p. 78
The cobordism ring [Omega]p. 81
The index of a 4 k-dimensional manifoldp. 84
The virtual indexp. 86
The Todd genus
Definition of the Todd genusp. 91
The virtual generalised Todd genusp. 94
The T-characteristic of a GL (q, C)-bundlep. 96
Split manifolds and splitting methodsp. 100
Multiplicative properties of the Todd genusp. 107
The Riemann-Roch theorem for algebraic manifolds
Cohomology of compact complex manifoldsp. 114
Further properties of the [actual symbol not reproducible]- characteristicp. 128
The virtual [actual symbol not reproducible]-characteristicp. 132
Some fundamental theorems of Kodairap. 138
The virtual [actual symbol not reproducible]-characteristic for algebraic manifoldsp. 142
The Riemann-Roch theorem for algebraic manifolds and complex analytic line bundlesp. 147
The Riemann-Roch theorem for algebraic manifolds and complex analytic vector bundlesp. 155
Appendix One by R. L. E. Schwarzenberger
Applications of the Riemann-Roch theoremp. 159
The Riemann-Roch theorem of Grothendieckp. 166
The Grothendieck ring of continuous vector bundlesp. 176
The Atiyah-Singer index theoremp. 184
Integrality theorems for differentiable manifoldsp. 196
Appendix Two: by A. Borel
A spectral sequence for complex analytic bundlesp. 202
Bibliographyp. 218
Indexp. 227
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540586630
ISBN-10: 3540586636
Series: Classics in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 234
Published: February 1995
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.35
Weight (kg): 0.36
Edition Number: 2

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