Non-simple genus minimizers in lens spaces

2013/05/02 by Joshua Evan Greene, Greene, Joshua Evan, Yi Ni +1
Mathematics · #57M25 #57M27 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1305.0517

openalex publication_date 2013/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Floer homology and knot complements
• Lens space surgeries and L-space homology spheres
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds
• One-sided and two-sided Heegaard splittings

Related

• Heegaard Floer correction terms and rational genus bounds
• Rational genus and Heegaard Floer homology
• The lens space realization problem
• Counting genus one fibered knots in lens spaces
• A number theoretic result for Berge's conjecture