In Hirsch's Differential Topology, he defines a smooth manifold $M$ to be reversable if it is orientable and admits an orientation-reversing diffeomorphism. I feel confused since I believe that any orientable manifold should admit one such diffeomorphisms. Are there any counter-examples for this?
2026-03-25 05:59:52.1774418392
Oriented but not Reversible manifolds?
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