Rational cobordisms and integral homology

 In the first part of the talk we give an introduction to rational homology cobordisms of 3-manifolds. We discuss several examples

and introduce the integral and rational homology spheres groups. We state several properties and open problems regarding these groups.

In the second half of the talk we show that lens spaces minimize the order of the first homology groups in their rational cobordism class. 

We explain several consequences of this fact and illustrate the strategy of the proof which relies on Donaldson's Diagonalization Theorem.

These results are part of a joint project with Daniele Celoria and JungHwan Park.