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Fibered, homotopy ribbon knots and the Poincaré Conjecture, I

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Jeffrey Meier
Western Washington University
Mon, 2019-09-09 15:00 - 16:00
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

A homotopy 4-sphere that is built without 1-handles can be encoded as a $n$-component link with an integral
Dehn surgery to $\#^n(S^1\times S^2)$.  I'll describe a program to prove that such spheres are smoothly standard
in the case that $n=2$ and one component of the link is fibered, which has been carried out in joint work with Alex Zupan in the case that the fibered knot is a generalized square knot.  I'll discuss how this relates to the problem of classifying ribbon disks for a fibered knot, and, time permitting, I'll outline how the theory of trisections connects this work to the Andrews-Curtis Conjecture and the Generalized Property R Conjecture. 

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