Every genus one algebraically slice knot is 1-solvable
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- by Christopher W. Davis, Taylor Martin, Carolyn Otto and JungHwan Park PDF
- Trans. Amer. Math. Soc. 372 (2019), 3063-3082 Request permission
Abstract:
Cochran, Orr, and Teichner developed a filtration of the knot concordance group indexed by half integers called the solvable filtration. Its terms are denoted by $\mathcal {F}_n$. It has been shown that $\mathcal {F}_n/\mathcal {F}_{n.5}$ is a very large group for $n\ge 0$. For a generalization to the setting of links the third author showed that $\mathcal {F}_{n.5}/\mathcal {F}_{n+1}$ is non-trivial. In this paper we provide evidence for knots $\mathcal {F}_{0.5}=\mathcal {F}_1$. In particular we prove that every genus 1 algebraically slice knot is 1-solvable.References
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Additional Information
- Christopher W. Davis
- Affiliation: Department of Mathematics, University of Wisconsin–Eau Claire, Eau Claire, Wisconsin 54701
- MR Author ID: 958152
- Email: daviscw@uwec.edu
- Taylor Martin
- Affiliation: Department of Mathematics, Sam Houston State University, Hunstville, Texas 77340
- MR Author ID: 1196069
- Email: taylor.martin@shsu.edu
- Carolyn Otto
- Affiliation: Department of Mathematics, University of Wisconsin–Eau Claire, Eau Claire, Wisconsin 54701
- MR Author ID: 804402
- Email: ottoa@uwec.edu
- JungHwan Park
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
- MR Author ID: 1188099
- Email: junghwan.park@math.gatech.edu
- Received by editor(s): March 13, 2017
- Received by editor(s) in revised form: February 12, 2018
- Published electronically: May 30, 2019
- Additional Notes: The fourth author was partially supported by the National Science Foundation grant DMS-1309081.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 3063-3082
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/tran/7682
- MathSciNet review: 3988602