Miriam Kuzbary (Amherst College)
Event Date
2025-03-28
Event Time
02:00 pm ~ 03:00 pm
Event Location
DRL Building, University of Pennsylvania
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Background talk (10am): Thinking about dimension 4, stuck in dimension 3: Knots, Concordances, and Homology Cobordisms
Abstract: It is a common theme in topology to study n-manifolds based on the n-1-manifolds they bound, or the n+1-manifolds bounded by them. We’ll explore together why this is an interesting and useful thing to do in dimensions 3 and 4! More specifically, we will talk about knots in the 3-sphere which are secretly related in 4-dimensional ways and how this can help us think about 3-manifolds that are similarly mysteriously connected.
Research talk (2pm): 0-Surgeries on Links
Abstract: In work in progress with Ryan Stees, we show that every closed, oriented 3-manifold can be obtained by 0-surgery on a link. Since the 0-surgery of a link can capture the data of many of the typical isotopy and concordance invariants of a link, particularly in the pairwise linking number 0 case, this result gives us a nice lens through which to study both 3-manifolds and links. However, 0-surgery on a link is certainly not a complete link invariant, and we also give multiple constructions for non-isotopic (and even non-concordant) links with homeomorphic 0-surgeries.