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A note on 0-bipolar knots of concordance order two


Author: Wenzhao Chen
Journal: Proc. Amer. Math. Soc. 147 (2019), 1773-1780
MSC (2010): Primary 57M25
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$.


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Additional Information

Wenzhao Chen
Affiliation: Department of Mathematics, Michigan State University, 619 Red Cedar Road, C535 Wells Hall, East Lansing, Michigan 48824
Email: chenwenz@msu.edu

DOI: https://doi.org/10.1090/proc/14315
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
Article copyright: © Copyright 2018 American Mathematical Society