Computing of Characteristic Classes and Spinors of Fiber Bundles

Abstract

We discussed some mathematical tools. We defined the topology of fiber bundles, geometry of characteristic classes, and its properties and computation in algebraic topology. The importance of characteristic classes and how they develop the cohomology theory as classification method has been treated. We use previous concepts related to gauge theories, Dirac operator and spinor structures as concrete applications of mathematics to physics and answer some questions in mathematical physics.