On equivariant deformation of maps (Q1105868)

Let G be a finite group acting on a simply-connected closed manifold X, let A be a closed invariant submanifold of X, and let f: (X,A)\(\to (X,A)\) be a G-map which is fixed point free on A. The author defines an obstruction set such that f is equivariantly deformable, relative to A, to a fixed point free G-map of X if and only if O belongs to the obstruction set. In the case that G acts freely on X-A and A is of codimension at least 3, the obstruction set is a single element which is zero if and only if the Lefschetz number of the homomorphism induced by f: (X,A)\(\to (X,A)\) is zero. A theory of equivariant deformations to fixed point free maps, for more general settings where X is not necessarily simply-connected nor the action on X-A free, has been developed by \textit{E. Fadell} and \textit{P. Wong} [Pac. J. Math. 132, No.2, 277-281 (1988; Zbl 0639.58009)].