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Thesis Defense
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Kai Nakamura, PMA 12.166: A classical approach to knot traces
Wednesday, May 15, 2024, 02:00pm - 03:00pm
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
Location: PMA 12.166

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