Euler Class
The Euler Class is a topological invariant associated with vector bundles, particularly in the field of algebraic topology. It provides a way to measure the "twisting" of a vector bundle over a manifold, helping to understand its geometric properties. The Euler Class is particularly significant in the study of differential geometry and characteristic classes.
In practical terms, the Euler Class can be computed for a given vector bundle, and it is often represented in cohomology theory. It plays a crucial role in various applications, including index theory and topological invariants, where it helps classify different types of manifolds and their properties.