2:00 pm Wednesday, May 15, 2024
Thesis Defense: A classical approach to knot traces by Kai Nakamura in PMA 12.166
Knot traces have quickly garnered intense interest following Piccirillo's proof that the Conway knot is not slice. We examine this hot topic of interest through a classical lens using well known techniques such as blowing up and down, turning a Kirby diagram upside down, and torus surgeries. This approach has led to several important applications. First, we rule out several potential counterexamples to the smooth $4$-dimensional Poincare Conjecture constructed by Manolescu and Piccirillo. Next, we show that a family of homotopy 4-spheres are standard. Then we show that the Manolescu and Piccirillo's construction can be successfully used to construct exotic elliptic surfaces. Finally, we construct a family of exotic knot traces with many novel properties. This is a thesis defense Submitted by
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