Heegaard Splittings and Complexity of Fibered Knots
Cengiz, Mustafa. “Heegaard Splittings and Complexity of Fibered Knots”, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108729.
This dissertation explores a relationship between fibered knots and Heegaard splittings in closed, connected, orientable three-manifolds. We show that a fibered knot, which has a sufficiently complicated monodromy, induces a minimal genus Heegaard splitting that is unique up to isotopy. Moreover, we show that fibered knots in the three-sphere has complexity at most 3.