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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on $0$-bipolar knots of concordance order two
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by Wenzhao Chen PDF
Proc. Amer. Math. Soc. 147 (2019), 1773-1780 Request permission

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
  • 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