Homotopy invariance is a fundamental property in algebraic topology that asserts that certain topological invariants remain unchanged under homotopy equivalences. This means if two spaces can be continuously deformed into each other, their associated algebraic structures, such as homology groups or chain complexes, will be the same. This idea is crucial for understanding how topological spaces relate to each other through continuous transformations and forms the backbone of various concepts in algebraic topology.
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