Math Colloquia

Date | Nov 28, 2024 |
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Speaker | 김민훈 |

Dept. | 이화여자대학교 |

Room | 129-101 |

Time | 16:00-17:00 |

In 2009, Calegari constructed smooth homotopy 4-spheres arising from an infinite collection of automorphisms of free groups including monodromies of fibered knots in the 3-sphere. We prove that all of these homotopy 4-spheres are diffeomorphic to the standard 4-sphere. Our result implies that the work of Casson and Gordon on homotopy ribbon fibered knots gives a large family of potential counterexamples to the smooth 4-dimensional Schoenflies conjecture. Our method builds on 5-dimensional handlebody arguments and the 3-dimensional Poincare conjecture. This is joint work with Jae Choon Cha.

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