2009 Topology Seminar - 04

An orientable manifold is called amphicheiral if it admits an orientation-reversing self-map and chiral if it does not. Many familiar manifolds like spheres or orientable surfaces are amphicheiral but chiral manifolds have also been known for many decades, e.g. the complex projective spaces CP^{2n} and some lens spaces in dimensions congruent 3 mod 4. Interestingly, however, this phenomenon had not been studied systematically. In my talk, I will report on results concerning both chirality and amphicheirality of manifolds. The focus lies on the existence of simply-connected chiral manifolds in all possible dimensions.