Topological Methods in Algebraic GeometrySpringer, 11 nov. 2013 - 232 pages |
Table des matières
| 1 | |
| 8 | |
Sheaves | 46 |
Fibre bundles | 50 |
Characteristic classes | 51 |
Chapter Two The cobordism ring | 76 |
PONTRJAGIN numbers 6 The ring 2 | 78 |
The cobordism ring 2 | 80 |
The virtual xcharacteristic | 135 |
Some fundamental theorems of KODAIRA | 138 |
The virtual characteristic for algebraic manifolds | 143 |
The RIEMANNROCH theorem for algebraic manifolds and complex analytic line bundles | 147 |
The RIEMANNROCH theorem for algebraic manifolds and complex analytic vector bundles | 155 |
Appendix One by R L E SCHWARZENBERGER 22 Applications of the RIEMANNROCH theorem | 159 |
The RIEMANNROCH theorem of GROTHENDIECK | 166 |
The GROTHENDIECK ring of continuous vector bundles | 176 |
The index of a 4kdimensional manifold | 84 |
The virtual index | 86 |
Chapter Three The TODD genus 10 Definition of the TODD genus | 91 |
The virtual generalised TODD genus | 94 |
The Tcharacteristic of a GL q Cbundle | 96 |
Split manifolds and splitting methods | 100 |
Multiplicative properties of the TODD genus | 107 |
Chapter Four The RIEMANNROCH theorem for algebraic manifolds 15 Cohomology of compact complex manifolds | 114 |
Further properties of the Xcharacteristic | 128 |
The ATIYAHSINGER index theorem 26 Integrality theorems for differentiable manifolds | 199 |
Appendix Two by A BOREL A spectral sequence for complex analytic bundles Bibliography | 202 |
| 218 | |
| 220 | |
91 | 221 |
96 100 | 222 |
| 228 | |
Autres éditions - Tout afficher
Expressions et termes fréquents
algebraic manifold analytic line bundles analytic sheaves analytic vector analytic vector bundle arithmetic genus associated b₁ C)-bundle c₁ c₂ CHERN classes cobordism coefficients cohomology class cohomology groups compact complex manifold complex analytic line complex analytic vector complex manifold complex vector bundles complex vector space corresponding d₁ defined definition denoted differentiable manifold differential operator dimension dimensional element embedding equation exact sequence F₁ fibre bundle finite follows formula generalisation H¹(X HIRZEBRUCH homomorphism h implies index theorem integer isomorphism KODAIRA Lemma LIE group line bundle m-sequence Math morphism open covering open neighbourhood open set oriented differentiable manifold oriented manifolds P₂ paracompact space polynomial PONTRJAGIN classes power series presheaf principal bundle prove RIEMANN-ROCH theorem ring SERRE sheaf of germs structure group subgroup submanifold tangent bundle TODD genus topological space U₁ V₁ vector space virtual zero