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Homology spheres and property R


Authors: Min Hoon Kim and JungHwan Park
Journal: Proc. Amer. Math. Soc. 149 (2021), 1323-1328
MSC (2020): Primary 57K10, 57K31, 57K32
DOI: https://doi.org/10.1090/proc/15299
Published electronically: December 31, 2020
MathSciNet review: 4211884
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Abstract | References | Similar Articles | Additional Information

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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References
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Additional 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
Article copyright: © Copyright 2020 American Mathematical Society