2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/39206We consider a lattice implementation of the eta-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating five-dimensional gauge field. We clarify the relation to the effective action for chiral Ginsparg-Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on the lattice with a finite spacing. A lattice expression for the five-dimensional Chern-Simons term is obtained.38 pages, LaTeX, revised versionHigh Energy Physics - LatticeHigh Energy Physics - Theorytext