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  "body": "\n## Summary\n\nThe eta invariant of a self-adjoint elliptic operator on a closed manifold measures the asymmetry of its spectrum between positive and negative eigenvalues.\nIt is the value at $s = 0$ of the eta function $\\sum \\operatorname{sign}(\\lambda) \\abs{\\lambda}^{-s}$, defined by analytic continuation.\nAtiyah, Patodi and Singer introduced it as the boundary correction in their [[index theorem for manifolds with boundary|GGFAH1M80J]].\n\n## Explanations\n\n### L1 human\n\nA self-adjoint operator has real eigenvalues, some positive and some negative, usually infinitely many of each.\nOne would like to count the positive ones minus the negative ones, but both counts are infinite.\nThe eta invariant is a regularized value of this difference, obtained by weighting each eigenvalue by $\\abs{\\lambda}^{-s}$ and continuing to $s = 0$.\nIf the spectrum is symmetric about $0$, the eta invariant is $0$.\n",
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