%0 Journal Article %T Orientation reversal of manifolds %A Daniel M¨šllner %J Mathematics %D 2009 %I arXiv %R 10.2140/agt.2009.9.2361 %X 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 -1. We prove that there are strongly chiral, smooth manifolds in every oriented bordism class in every dimension greater than two. We also produce simply-connected, strongly chiral manifolds in every dimension greater than six. For every positive integer k, we exhibit lens spaces with an orientation-reversing self-diffeomorphism of order 2^k but no self-map of degree -1 of smaller order. %U http://arxiv.org/abs/0907.5283v2