Nikolay Tyurin: Standard and exotic homological spheres
In certain approach to cosmological problems one uses Poincare homological spheres. These compact manifolds look similiar to standard sphere on the “commutative level” having the same homology groups. But in constrast with the standard sphere these new exotic objects have non trivial fundamental group. In my lectures I present some history on the subject and construct several examples (on rather simple and explicit level) of the homological spheres.