2019/12/30 by Mustafa Cengiz, Cengiz, Mustafa
Mathematics · Medicine · Biochemistry, Genetics and Molecular Biology · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders #Connective tissue disorders research
paper · pdf · doi:10.48550/arxiv.1912.13019
We prove that if a fibered knot K with genus greater than one in a three-manifold M has a sufficiently complicated monodromy, then K induces a minimal genus Heegaard splitting P that is unique up to isotopy, and small genus Heegaard splittings of M are stabilizations of P. We provide a complexity bound in terms of the Heegaard genus of M. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.