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Orientation reversal of manifolds Summary of my PhD thesis

Manifolds which do not allow orientation-reversing maps to themselves have been known for a long time. Textbook examples are the complex projective spaces CP2n in dimensions that are divisible by 4 and some lens spaces in dimensions congruent 3 modulo 4. Apart from these well-known examples, only sparse results were known (see below for some of them), so my PhD project is dedicated to the following question: