Serre Spectral Sequence
The Serre Spectral Sequence is a powerful tool in algebraic topology that helps compute the homology or cohomology of a space with a fibration. It organizes information about the fibers, base space, and total space into a sequence of abelian groups, allowing mathematicians to analyze complex topological structures systematically.
This sequence arises from a fibration, which is a special type of mapping between spaces. The E_2 page of the sequence captures the relationships between the homology of the base space and the fibers, leading to a deeper understanding of the overall topology of the total space.