This article is cited in 3 papers

Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group

K. N. Zhuikov, A. Yu. Savin

Peoples' Friendship University of Russia, Moscow

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.

Keywords: elliptic operator, parameter-dependent operator, nonlocal operator, $\eta$-invariant.

UDC: 515.168.5

Received: 02.06.2022

DOI: 10.4213/mzm13778

 English version: Mathematical Notes, 2022, 112:5, 685–696

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