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Cohomology and Differential Forms
This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology.
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the ÄŒech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
mathematics;abelian categories;fiber bundles;vector bundles;riemannian manifolds;de rham;allendoerfer eells;dolbeault serre;nonfiction;mathematical research;cohomology;cohomological theory of manifolds;differential forms;differential mathematics;differential geometry;global analysis;topology;geometry;cohomological theory;various sheaves;chern classes;cochain;coefficients;harmonic forms;science and math;physics;science
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the ÄŒech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
Reprint with minor corrections of the Marcel Dekker, Inc., New York, 1973 edition.Â
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Description
This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology.
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the ÄŒech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
mathematics;abelian categories;fiber bundles;vector bundles;riemannian manifolds;de rham;allendoerfer eells;dolbeault serre;nonfiction;mathematical research;cohomology;cohomological theory of manifolds;differential forms;differential mathematics;differential geometry;global analysis;topology;geometry;cohomological theory;various sheaves;chern classes;cochain;coefficients;harmonic forms;science and math;physics;science
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the ÄŒech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
Reprint with minor corrections of the Marcel Dekker, Inc., New York, 1973 edition.Â
