A relative index theorem (Q5943431)

For a Dirac operator the author introduces the notion to be \textit{non-parabolic at infinity.} This yields a sufficient condition for a relative index theorem extending results by \textit{M. Gromov} and \textit{H. B. Lawson} [Publ. Math., Inst. Hautes Étud. Sci. 58, 83--196 (1983; Zbl 0538.53047)] and \textit{H. Donnelly} [J. Funct. Anal. 75, 362--381 (1987; Zbl 0634.58031)]. As an application an index theorem is presented for manifolds with finitely many ends which are Riemannian products of a compact manifold and the complement of a ball in an Euclidean space.