
02/27 4:00pm 
BLOC 624 
Maggie Miller University of Texas at Austin 
Branched covers of twistroll spun knots
Twistroll spun knots are a family of 2spheres that are smoothly knotted in the 4sphere. Many of these 2spheres are known to be branch sets of cyclic covers of the 4sphere over itself (maybe counterintuitively to 3dimensional topologists, since this never happens for nontrivial knots in the 3sphere). It’s very difficult to come up with interesting examples of 2spheres in the 4sphere, so this family typically serves as the examples in any theorem about surfaces in the 4sphere. I’ll discuss a few different versions of their construction and prove a relationship between some of their branched coverings. As a corollary, we’ll conclude that some interesting families of manifolds known to be homeomorphic are actually diffeomorphic. This is joint with Mark Hughes and Seungwon Kim.
