流形的方向反转
Orientation reversal of manifolds
摘要：
如果一个闭的、连通的、可定向流形在TOP、PL或DIFF范畴之一中不允许方向反转的自同构，则称它为手征流形，否则称它为双手征流形。此外，我们称一个流形为强手征流形，如果它不允许一个-1次的自映射。证明了在大于2的维数上，每个定向边形类中都存在强手征的光滑流形。我们还产生了简单连接，强手征流形在每一个维度大于6。对每一个正整数k，我们证明了透镜空间具有2^k阶的方向反转自同构，但不具有更小阶的-1次自映射.
英文摘要：
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.
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