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### Degree of a virtual covering map and harmonic map to the circle

**Geometry/Topology**

Speaker: | Inkang Kim, Korea Institute of Advanced Study |

Location: | Zoom |

Start time: | Tue, Jun 1 2021, 1:10PM |

Thurston conjectured that any finite volume hyperbolic 3-manifold has a virtual cover which fibers over the circle, which is answered positively by Ian Agol. But it is not easy to determine how large the degree of the virtual cover is.

Using a simple differential geometric technique involving harmonic maps, we give a lower bound for the degree of a virtual cover, which fibers over the circle, of a closed hyperbolic 3-manifold.

As an another application, we give a positive answer to a question raised by Gromov about the Euclidean cube in dimension 3.