Subject: A question for the list From: Daniel Müllner Date: Tue, 31 Jan 2006 09:12:42 +0100 Is there anything known related to the following question: When does a (closed, orientable) manifold disallow an orientation reversing self- diffeomorphism? (Likewise: Homeomorphism? Homotopy self-equivalence?) Or simpler: In which dimensions exist manifolds that have no orientation reversing diffeomorphism? If the dimension is divisible by four we have a symmetric intersection form and Pontrjagin numbers, so there are well-known examples of manifolds of this type (e.g. every CP^{2n}). In dimensions 3 modulo 4, the linking form gives restrictions so that one can rule out some lens spaces. But what about dimensions 1 and 2 mod 4? Except for the simple examples mentioned above, which are known for some decades, I could not find any result in the literature. On the other hand, the question seems quite natural to me, so I expect that someone has already thought further, and maybe there are some results. Thank you in advance for any references and helpful thoughts, Daniel Müllner