Mayer-Vietoris sequence

The Mayer-Vietoris sequence is a mathematical tool used in algebraic topology to analyze the shape of complex objects. It breaks down a complicated space into overlapping simpler parts, then uses information from these parts and their overlaps to understand the entire object’s structure. Think of it like dividing a puzzle into sections, examining each piece and how they fit together, to figure out the whole picture. This sequence helps mathematicians compute topological features (like holes and connectivity) of complex spaces by relating them to those of their simpler components.