Low Dimensional Topology & Circle-valued Morse Functions

Explore advanced concepts in knot theory and low-dimensional topology in this 57-minute conference talk by Allison Moore from Virginia Commonwealth University. Delve into tangle decompositions of knots and links along Conway spheres, and discover how Khovanov homology can be calculated and approached using these decompositions. Learn about the translation of algebraic invariants associated with tangles into sets of immersed curves on the four-punctured sphere. Understand the application of this strategy in investigating two classic open problems: the cosmetic surgery conjecture and the cosmetic crossing conjecture. Gain insights into collaborative research efforts with Kotelskiy, Lidman, Watson, and Zibrowius in this cutting-edge exploration of low-dimensional topology.