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### Khovanov skein lasagna module detects exotic 4-manifolds

**Geometry/Topology**

Speaker: | Qiuyu Ren, UC Berkeley |

Related Webpage: | https://math.berkeley.edu/~qiuyu/ |

Location: | 2112 MSB |

Start time: | Tue, Mar 5 2024, 2:10PM |

We present new calculations of the Khovanov-Rozansky $gl_2$ skein lasagna modules defined by Morrison-Walker-Wedrich, generalizing several previous works. In particular, our calculation shows that the -1 traces on the knots $-5_2$ and $P(3,-3,-8)$ have non-isomorphic skein lasagna modules, thus are non-diffeomorphic (while they are homeomorphic by Kirby moves + Freedman's result). This leads to the first gauge/Floer-theory-free proof of the existence of compact exotic 4-manifolds. Time permitting, we sketch some proofs of our calculation results. This is joint work with Michael Willis.