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### Four-genus bounds from the 10/8+4 theorem

**Geometry/Topology**

Speaker: | Linh Truong, University of Michigan |

Location: | 2112 MSB |

Start time: | Tue, Feb 13 2024, 2:10PM |

Donald and Vafaee

constructed a knot slicing obstruction for knots in the three-sphere by producing a bound relating the signature and second Betti number of a spin 4-manifold whose boundary is zero-surgery on the knot. Their bound relies on Furuta's 10/8 theorem and can be improved with the 10/8 + 4 theorem of Hopkins, Lin, Shi, and Xu. I will explain how to expand on this technique to obtain four-ball genus bounds and compute the bounds for some satellite knots. This is joint work in progress with Sashka Kjuchukova and Gordana Matic.