The spectral sequence of a fibration is a powerful tool in algebraic topology that arises when dealing with fibrations, allowing one to compute the homology or cohomology groups of a fiber space by examining the relationships between the spaces involved. It provides a systematic way to organize complex information about how the spaces interact, often leading to significant simplifications in computations. This tool connects different levels of topology, revealing how the structure of fibrations can be explored through spectral sequences.
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