An introduction to the rational genus of a knot

An introduction to the rational genus of a knot

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Zhongtao Wu, Caltech
Fine Hall 314

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.