Cohomology and Differential Forms (Dover Books on Mathematics) - Softcover

Vaisman, Izu

Softcover

ISBN 10: 0486804836 ISBN 13: 9780486804835

Publisher: Dover Publications, 2016

Synopsis

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.

About this title

About the Author

Izu Vaisman is Professor Emeritus of Mathematics at the University of Haifa. His research areas are differential geometry and symplectic manifolds, and his other books include Analytical Geometry, Foundations of Three Dimensional Euclidean Geometry, and A First Course in Differential Geometry.

From the Back Cover

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.
Dover (2016) republication with minor corrections of the edition originally published by Marcel Dekker, Inc., New York, 1973.
www.doverpublications.com

Edition details

• Publisher: Dover Publications
• Publication date: 2016
• Language: English
• ISBN 10: 0486804836
• ISBN 13: 9780486804835
• Binding: Paperback
• Number of pages: 304