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### Two-fold branched covers

**Geometry/Topology**

Speaker: | Dave Auckly |

Location: | 2112 MSB |

Start time: | Wed, Oct 27 2010, 4:10PM |

It is possible to give a census of 2-fold branched covering behavior for surgeries on knots of 10 or fewer crossings. There are integral homology spheres that are not 2-fold branched covers of any 3-manifold, there are examples that are 2-fold branched covers of $S3$ but no other manifold, examples that cover some manifold but not S3, and examples that cover several different manifolds. This talk will present these examples. Thurston asked if any every closed, irreducible, atoroidal 3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle. This is the virtual fibering conjecture. The presentation will also include a virtual virtual fibering result showing that the answer is yes if cover is replaced by branched cover.