Cohomology and Differential Forms

Book Details

• Publisher: Dover

• Author: Izu Vaisman

• Language: English

• Edition: 1st Edition

• ISBN: 9780486804835

• Pages: 284

• Cover: Paperback

• Dimensions: 8.9 x 6.0 x 0.7 inches

About The Book

"Izu Vaisman’s Cohomological Theory of Manifolds and Sheaves" is a scholarly monograph that delves deep into the cohomological theory of manifolds equipped with various sheaves, and its profound applications within differential geometry. This book is grounded in lectures delivered by the author at the University of Iasi in Romania and is designed for advanced undergraduates, graduate students, and researchers in the fields of mathematics, particularly those specializing in differential geometry, global analysis, and topology.

The book offers a self-contained development of cohomological theory, making it an invaluable resource for students and scholars alike. It covers a range of essential topics, including categories and functors, Čech cohomology with sheaf coefficients, fiber bundle theory, and the study of differentiable, foliated, and complex analytic manifolds. The final chapter explores the theorems of de Rham and Dolbeault-Serre, and further investigates the theorem of Allendoerfer and Eells, applying these theorems to characteristic classes and the broader theory of harmonic forms.

Through clear explanations and methodical presentation, Vaisman’s work provides an essential framework for understanding these advanced mathematical concepts, making it an indispensable tool for anyone involved in the study or research of manifold theory and cohomology.