Modern Differential Geometry in Gauge Theories

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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.