On strongly inflexible manifolds

TL;DR

This paper investigates the existence of simply-connected strongly inflexible manifolds, providing an algorithm based on Sullivan models that shows most known examples of simply-connected inflexible manifolds are not strongly inflexible.

Contribution

It introduces an algorithm using Sullivan models to analyze inflexibility and demonstrates that most known simply-connected inflexible manifolds are not strongly inflexible.

Findings

Most known simply-connected inflexible manifolds are not strongly inflexible.

An algorithm based on Sullivan models can determine inflexibility properties.

Open question remains about the existence of simply-connected strongly inflexible manifolds.

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 allow us to prove that all, but one, of the known examples of simply-connected inflexible manifolds are not strongly inflexible.