K-theory invariants are algebraic objects that arise in the study of vector bundles and topological spaces, providing a way to classify these bundles in terms of their stable equivalence. They are essential for understanding various properties of topological insulators, as they can capture the non-triviality of electronic states in condensed matter physics. This makes k-theory invariants a powerful tool for distinguishing between different phases of matter and understanding phenomena like edge states and gaps in energy levels.
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