Published April 23, 2015
| Submitted
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Non-simple genus minimizers in lens spaces
- Creators
- Greene, Joshua Evan
- Ni, Yi
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.
Additional Information
We thank Ian Agol, Ken Baker, Josh Batson, Cameron Gordon, Adam Levine, Danny Ruberman, and Sucharit Sarkar for helpful discussions. We especially thank Eli Grigsby for providing her computer program to compute knot Floer homology of knots in lens spaces. We also thank the Simons Center for Geometry and Physics and the organizers of the workshop "Symplectic and Low Dimensional Topologies in Interaction" for providing an ideal place for us to collaborate. The first author was partially supported by NSF grant number DMS-1207812. The second author was partially supported by NSF grant number DMS-1103976 and an Alfred P. Sloan Research Fellowship.Attached Files
Submitted - 1305.0517.pdf
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Additional details
- Eprint ID
- 56821
- Resolver ID
- CaltechAUTHORS:20150421-115844735
- DMS-1207812
- NSF
- DMS-1103976
- NSF
- Alfred P. Sloan Foundation
- Created
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2015-04-23Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field