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Genus minimizing knots in rational homology spheres

4:00 pm Thursday, March 13, 2013
Yi Ni (Caltech)

It has been known that the Donaldson-Floer type invariants for 3- and 4-manifolds can be used to give lower bound to the genus of surfaces representing a given homology class. In this talk, we will discuss a new type of genus bounds from Heegaard Floer homology, which gives a lower bound to the rational genus of all knots in a given torsion homology class. Such genus bounds are related to problems like lens space surgery, one-sided Heegaard splitting, and complexity of 3-manifolds. This talk is based on joint work with Zhongtao Wu and with Josh Greene.

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