On Strongly Inflexible Manifolds

Abstract

Abstract An oriented closed connected $N$-manifold $M$ is inflexible if it does not admit self-maps of unbounded degree. In addition, if all the maps from any other oriented closed connected $N$-manifold have bounded degree, then $M$ is said to be strongly inflexible. The existence of simply-connected inflexible manifolds was established by Arkowitz and Lupton. However, the existence of simply-connected strongly inflexible manifolds is still an open question. We provide an algorithm relying on Sullivan models that allows us to prove that all, but one, of the known examples of simply-connected inflexible manifolds are not strongly inflexible.