Abstract
\(\eta\)-invariants for a class of parameter-dependent nonlocal operators associated with an isometric action of a discrete group of polynomial growth on a smooth closed manifold are studied. The \(\eta\)-invariant is defined as the regularization of the winding number. The formula for the variation of the \(\eta\)-invariant when the operator changes is obtained. The results are based on the study of asymptotic expansions of traces of parameter-dependent nonlocal operators.
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The work was supported in part by Young Russian Mathematics award as well as by RFBR and DFG, project number 21-51-12006.
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Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 705–717 https://doi.org/10.4213/mzm13778.
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Zhuikov, K.N., Savin, A.Y. Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group. Math Notes 112, 685–696 (2022). https://doi.org/10.1134/S0001434622110062
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DOI: https://doi.org/10.1134/S0001434622110062