Uniform bounds for equivariant homotopies

AbstractIn this paper our previous joint work with Calder on the width of homotopies into compact Riemannian manifolds with finite fundamental groups is extended to the equivariant setting. We produce necessary conditions under which the widths of equivariant homotopies are bounded and characterize these equivariant bounds in terms of the fixed point submanifolds of the action. Finally, we apply these results to covering spaces to relate the (non-equivariant) bounds for a manifold with finite fundamental group to those of its universal covering space