The eta invariant is a topological invariant associated with a self-adjoint elliptic operator, which provides important information about the geometry and topology of manifolds. This invariant plays a key role in various areas of mathematics, especially in K-theory and in understanding fixed point theorems, as well as in applications stemming from Bott periodicity. By quantifying certain features of the spectrum of an operator, the eta invariant can help in studying the behavior of manifolds under various transformations.
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