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Algebraic Topology

Algebraic topology provides another example of the interaction. Topology is a different, more flexible, kind of geometry, where objects are built out of discs and spheres rather than represented by equations. The search for algebraic invariants of such geometrical representations of spaces led to the field of algebraic topology. Efficient tools to study such invariants of topological spaces are provided by homotopy theory, whose techniques are nowadays used to understand many other types of mathematical objects.