North Meets South

Paolo Aceto

Knot concordance and homology cobordisms of 3-manifolds 

We introduce the notion of knot concordance for knots in the 3-sphere and discuss some key problems regarding the smooth concordance group. After defining homology cobordisms of 3-manifolds we introduce the integral and rational homology cobordism groups and briefly discuss their relationship with the concordance group. We conclude stating a few recent results and open questions on the structure of these groups.