Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

The authors wrote this book to demystify abstract concepts of algebraic geometry and homological algebra for a new generation of mathematicians, with a focus on cohomology and presheaves. It provides intuitive motivation and detailed proofs of key theorems.

Format: Hardback
Length: 800 pages
Publication date: 21 February 2022
Publisher: World Scientific Publishing Co Pte Ltd

For over three decades, the senior author has dedicated himself to the study of algebraic geometry, a field that has revealed the profound interconnectedness of cohomology, homological algebra, and sheaf theory. Recognizing the daunting challenges posed by these abstract concepts, he embarked on a mission to demystify them and make them accessible to a new generation of mathematicians. In collaboration with a co-author, he authored this comprehensive book, designed to cater to an audience familiar with the fundamentals of linear and abstract algebra but with limited exposure to algebraic geometry and homological algebra.

The book is structured into two parts. The first part serves as a crash course on the homological and cohomological aspects of algebraic topology, with a particular emphasis on cohomology. It aims to provide a solid foundation in these areas, emphasizing their significance and applications. The second part delves into presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. Each concept is intuitively motivated, and the corresponding proofs are presented in meticulous detail, often lacking in standard texts.

By offering a comprehensive and accessible approach, this book aims to bridge the gap between algebraic geometry and its related disciplines, enabling students to grasp these complex concepts and apply them in various fields of mathematics. Whether you are a student seeking to expand your knowledge or a professional looking to deepen your understanding of algebraic geometry, this book is a valuable resource that will guide you on your journey.

ISBN-13: 9789811245022