We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does not admit a self-map of degree . We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension . We also produce simply-connected, strongly chiral manifolds in every dimension . For every , we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order but no self-map of degree of smaller order.
"Orientation reversal of manifolds." Algebr. Geom. Topol. 9 (4) 2361 - 2390, 2009. https://doi.org/10.2140/agt.2009.9.2361