Anastasios Mallios Libros

This work presents a novel approach to differential geometry by employing an axiomatic framework that bypasses traditional calculus concepts. Instead of smooth manifolds, the author utilizes sheaf theory and sheaf cohomology to explore geometric physical theories. By focusing on vector sheaves derived from arbitrary topological spaces, the book offers fresh insights and calculations that open up new potential applications in the field. This perspective challenges conventional methods and enriches the understanding of differential geometry.

Focusing on fundamental concepts and results, this two-volume monograph delves into the standard differential geometry of smooth manifolds. It offers a comprehensive exploration of key theories and applications, catering to both advanced students and researchers in the field. The work emphasizes rigorous mathematical formulations and includes numerous examples to illustrate complex ideas, making it an essential resource for understanding the intricacies of differential geometry.

This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable