A note on the cobordism invariance of the index (Q808072)

Using the analysis of operators on complete manifolds and some argument due to J. Roe the author gives a simple proof of the cobordism invariance for the analytic index of Dirac type operators. In fact the author proves here even more then this - namely Roe's index theorem for partitioned manifolds [cf. \textit{J. Roe}, Lond. Math. Soc. Lect. Note Ser. 135, 187- 228 (1988; Zbl 0677.58042)].