Published November 2008
| Submitted
Journal Article
Open
On standard forms of 1-dominations between knots with same Gromov volumes
- Creators
- Boileau, Michel
- Ni, Yi
- Wang, Shicheng
Abstract
Let k and k′ be two knots in the 3-sphere. Say k 1-dominates k′, if there is a proper degree 1 map f: E(k) → E(k′). Theorem: Suppose that any companion of k is prime. If k 1-dominates k′ with the same Gromov volume, then k′ can be obtained from k by finitely many de-satellizations. The condition of "same Gromov volume" clearly cannot be removed. We also give a new construction of 1-domination between knots with the same Gromov volume to show that the condition "any companion of k is prime" cannot be removed.
Additional Information
© 2008 World Scientific Publishing Co. Received: 10 January 2008; Revised: 19 March 2008. This research was conducted during the periods the second author was a graduate student at Princeton University and was employed by the Clay Mathematics Institute as a Liftoff Fellow. The second author was partially supported by a Graduate School Centennial Fellowship at Princeton University. The third author is partially supported by grant No.10631060 of the National Natural Science Foundation of China.Attached Files
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Additional details
- Eprint ID
- 56824
- DOI
- 10.1142/S0219199708003071
- Resolver ID
- CaltechAUTHORS:20150421-115855236
- Clay Mathematics Institute
- Princeton University Centennial Fellowship
- 10631060
- National Natural Science Foundation of China
- Created
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2015-04-21Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field