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arXiv · 2307.03100

Note on a numerical equality regarding the eta invariant on Berger spheres

J. S. Dowker
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Abstract

The Dirac APS eta invariant on a Berger sphere of dimension $2n-1$ is discovered, numerically, to coincide, up to spin factors, with the Dirac conformal anomaly on a round sphere of even dimension, $n$. The analytical expression, given in terms of a generalised Bernoulli polynomial, is shown to equal a known conjecture for the eta invariant. Weingart's generating function is also obtained with no extra work.

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J. S. Dowker. 2023-07-06. Note on a numerical equality regarding the eta invariant on Berger spheres. https://arxiv.org/abs/2307.03100

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