# Almost Complex Structures on Rational Homology Spheres

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Michael Albanese

created by daniele on 27 Jun 2018

modified on 28 Jun 2018

4 jul 2018
-- 16:00

Aula Tricerri, DiMaI, Firenze

**Abstract.**

It is a well-known result that the only spheres which can admit almost complex structures occur in dimensions two and six. We show that if one instead considers rational homology spheres (manifolds with the same rational homology as a sphere), then the same conclusion holds: they can only admit almost complex structures in dimensions two and six. However, there are infinitely many six-dimensional rational homology spheres and not all of them admit almost complex structures. We will explain how to construct infinitely many examples which do admit almost complex structures and infinitely many which do not. This is joint work with Aleksandar Milivojevic.