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