Non-simple genus minimizers in lens spaces

Abstract

Given a one-dimensional homology class in a lens space, a question related to the Berge conjecture on lens space surgeries is to determine all knots realizing the minimal rational genus of all knots in this homology class. It is known that simple knots are rational genus minimizers. In this paper, we construct many non-simple genus minimizers. This negatively answers a question of Rasmussen.

16 pages, 6 figures

References in corpus (7)

• Floer homology and knot complements
• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Bridge number and integral Dehn surgery
• Small genus knots in lens spaces have small bridge number
• One-sided and two-sided Heegaard splittings
• Heegaard Floer correction terms and rational genus bounds

Cited by in corpus (1)

• Correction terms, ${\mathbb{Z}}_2$--Thurston norm, and triangulations