A note on $0$-bipolar knots of concordance order two
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- by Wenzhao Chen
- Proc. Amer. Math. Soc. 147 (2019), 1773-1780
- DOI: https://doi.org/10.1090/proc/14315
- Published electronically: December 12, 2018
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Abstract:
Let $\mathcal {T}$ be the group of smooth concordance classes of topologically slice knots, and let $\{0\}\subset \cdots \subset \mathcal {T}_{n+1}\subset \mathcal {T}_{n}\subset \cdots \subset \mathcal {T}_{0}\subset \mathcal {T}$ be the bipolar filtration. Hedden, Kim, and Livingston showed that $\mathcal {T}$ contains a subgroup isomorphic to $\mathbb {Z}_2^\infty$. In this paper, we show that a subset of the set of knots constructed by Hedden, Kim, and Livingston generates a subgroup isomorphic to $\mathbb {Z}_2^{\infty }$ in $\mathcal {T}_0/\mathcal {T}_1$.References
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Bibliographic Information
- Wenzhao Chen
- Affiliation: Department of Mathematics, Michigan State University, 619 Red Cedar Road, C535 Wells Hall, East Lansing, Michigan 48824
- MR Author ID: 1309566
- Email: chenwenz@msu.edu
- Received by editor(s): March 31, 2018
- Received by editor(s) in revised form: June 23, 2018, and July 5, 2018
- Published electronically: December 12, 2018
- Communicated by: David Futer
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1773-1780
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/proc/14315
- MathSciNet review: 3910441