An introduction to the rational genus of a knot
An introduction to the rational genus of a knot

Zhongtao Wu, Caltech
Fine Hall 314
What is the "simplest" knot in a given threemanifold $Y$? We know that the answer is the unknot when $Y=S^3$, as the unknot happens to be the only knot in the threesphere 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.