What is the "simplest" knot in a given three-manifold Y?
We know that the answer is the unknot when Y=S^3, as the unknot
happens to be the only knot in the three-sphere with the smallest
genus (=0). In this talk, we will discuss the more general notion of
the rational genus of knots. In particular, we will show that the
simple knots are really the "simplest" knots in the lens spaces in
the sense of being a genus minimizer in its homology class. This is
a joint work with Yi Ni.