Cohomology and differential forms
by Vaisman, Izu
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 inclu…
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- Full title :Cohomology and differential forms / Izu Vaisman, Department of Mathematics, University of Haifa, Haifa, Israel.
Summary
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 Čech 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.
Read More ↓Edition Statements
- Publication Date:2016.
Publication Statements
- Publisher(s):Dover Publications
- Place of Publication:Mineola, New York
- Language:eng
- Publication Date:2016.
Notes
"Translation editor: Samuel I. Goldberg, University of Illinois at Urbana-Champaigne, Urbana, Illinois"--Galley t.p. verso
Slightly corrected; originally published: New York : Marcel Dekker, Inc., 1973.
The Physical Object
- Description:1 online resource
Edition Identifiers
- ISBN:0486815129, 9780486815121
- oclc:ocn955136560
- LC Classification:QA649
- Dewey Decimal:516.36
Table of Contents
Categories and functors -- Sheaves and cohomology -- Fiber and vector bundles -- Differential geometry -- Cohomology classes and differential forms.
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