Equivariant cobordism, vector fields, and the Euler characteristic (Q1061392)

Let G be a finite group. For two closed G-manifolds M and N, a G- cobordism L between them is called a Reinhart G-cobordism if L admits a G-invariant nonzero vector field which is inward normal on M and outward normal on N. The aim of this paper is to obtain a necessary and sufficient condition for the existence of a Reinhart G-cobordism between two given G-cobordant closed G-manifolds. \textit{B. L. Reinhart} [Topology 2, 173-177 (1963; Zbl 0178.264)] is just the case in which G is the trivial group. When G is of odd order or of order 2, the author gives such a condition in terms of the Euler characteristic of fixed point sets with specified normal representations. The result is proved by altering a given G-cobordism to a Reinhart G-cobordism by equivariant surgery and connected sum. If G is of order 2, \textit{R. E. Stong} [Math. Ann. 26, 181- 196 (1975; Zbl 0303.57016)] obtained such a condition in some cases.