Exotic structures on 4-manifolds detected by spectral invariants (Q1110156)

In this paper the spectrum of the twisted Dirac operator on the exotic projective space \(Q^ 4\) constructed by \textit{S. E. Cappell} and \textit{J. L. Shaneson} [Ann. Math., II. Ser. 104, 61-72 (1976; Zbl 0345.57003)] is studied. This space is homeomorphic to the real projective space \(RP^ 4\), but not diffeomorphic to it. It is proved that the spectra of the twisted Dirac operator on \(RP^ 4\) resp. \(Q^ 4\) are never the same, independent of the metric chosen.