Topology Seminar

Date: February 27, 2024

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: Maggie Miller, University of Texas at Austin

Title: Branched covers of twist-roll spun knots

Abstract: Twist-roll spun knots are a family of 2-spheres that are smoothly knotted in the 4-sphere. Many of these 2-spheres are known to be branch sets of cyclic covers of the 4-sphere over itself (maybe counterintuitively to 3-dimensional topologists, since this never happens for nontrivial knots in the 3-sphere). It’s very difficult to come up with interesting examples of 2-spheres in the 4-sphere, so this family typically serves as the examples in any theorem about surfaces in the 4-sphere. 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.