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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Homology spheres and property R
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by Min Hoon Kim and JungHwan Park
Proc. Amer. Math. Soc. 149 (2021), 1323-1328
DOI: https://doi.org/10.1090/proc/15299
Published electronically: December 31, 2020
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Abstract:

We present infinitely many homology spheres which contain two distinct knots whose $0$-surgeries are $S^1 \times S^2$. This resolves a question posed by Kirby and Melvin in $1978$.
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Bibliographic Information
  • Min Hoon Kim
  • Affiliation: Department of Mathematics, Chonnam National University, Gwangju, Republic of Korea
  • MR Author ID: 1067137
  • Email: minhoonkim@jnu.ac.kr
  • JungHwan Park
  • Affiliation: Department of Mathematical Sciences, KAIST, 291 Daehak-ro Yuseong-gu, Daejeon, 34141, South Korea
  • MR Author ID: 1188099
  • Email: jungpark0817@gmail.com
  • Received by editor(s): April 28, 2020
  • Received by editor(s) in revised form: June 22, 2020
  • Published electronically: December 31, 2020
  • Additional Notes: This project started when the first named author was visiting the Georgia Institute of Technology and he thanks the Georgia Institute of Technology for its generous hospitality and support.
  • Communicated by: Shelley Harvey
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 1323-1328
  • MSC (2020): Primary 57K10, 57K31, 57K32
  • DOI: https://doi.org/10.1090/proc/15299
  • MathSciNet review: 4211884