Abstract
Using a formula from Donnelly (Indiana Univ Math J 27(6):889–918, 1978), we prove that for a family of seven dimensional flat manifolds with cyclic holonomy groups the η invariant of the signature operator is an integer number. We also present an infinite family of flat manifolds with integral η invariant. The main motivation is a paper of Long and Reid (Geom Topol 4:171–178, 2000).
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