On the topology of rooted forests in higher dimensions

In this paper, we prove that a 'punctured' closed, connected, orientable triangulated manifold is simple homotopy equivalent to any of its roots. We also emphasize that this phenomena does not hold in general. Orientability plays a central role for this result and thus makes the result interesting. In the course of the proof of this theorem, we prove two lemmas, which partially answer two questions of Olivier Bernardi and Caroline Klivans.