Georgia Institute of Technology College of Sciences

The set of knots up to a four-dimensional equivalence relation can be given the structure of a group, called the (smooth) knot concordance group. We will discuss how to compute concordance invariants using Heegaard Floer homology. We will then introduce the idea of a "reduced" knot Floer complex, see how it can be used to simplify computations, and give examples of how it can be helpful in distinguishing knots which are not concordant.