Heegaard genus and complexity of fibered knots. Issue 4 (8th November 2022)

• Record Type: Journal Article
• Authors: Cengiz, Mustafa
• Is Part Of: Journal of topology. Volume 15:Issue 4(2022)
• Page Start: 2389
• Page End: 2425
• Publication Date: 2022-11-08
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12268
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We prove that if a fibered knot K $K$ with genus greater than 1 in a three‐manifold M $M$ has a sufficiently complicated monodromy, then K $K$ induces a minimal genus Heegaard splitting P $P$ that is unique up to isotopy, and small genus Heegaard splittings of M $M$ are stabilizations of P $P$ . We provide a complexity bound in terms of the Heegaard genus of M $M$ . We also provide global complexity bounds for fibered knots in the three‐sphere and lens spaces.