English

Non-simple genus minimizers in lens spaces

Geometric Topology 2013-05-03 v1

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.

Keywords

Cite

@article{arxiv.1305.0517,
  title  = {Non-simple genus minimizers in lens spaces},
  author = {Joshua Evan Greene and Yi Ni},
  journal= {arXiv preprint arXiv:1305.0517},
  year   = {2013}
}

Comments

16 pages, 6 figures

R2 v1 2026-06-22T00:10:24.080Z