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Dehn surgery on ribbon knots

Aykut Arslan

Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA

https://doi.org/10.1142/S0218216517500675Cited by:0 (Source: Crossref)

Abstract

In this paper, we show that if 0-surgery along a ribbon knot $𝔰$ and 0-surgery along another knot $𝔟$ give diffeomorphic 3-manifolds then $𝔟$ has to be a slice knot. Moreover, they have diffeomorphic slice disk exteriors $D^{4} - N (D_{𝔰}^{2}) ≅ D^{4} - N (D_{𝔟}^{2})$ for some ribbon disk $D_{𝔰}^{2}$ and slice disk $D_{𝔟}^{2}$ , where $N (D_{𝔰}^{2})$ and $N (D_{𝔟}^{2})$ are tubular neighborhoods of $D_{𝔰}^{2}$ and $D_{𝔟}^{2}$ , respectively.

Keywords:

AMSC: 57M25, 57R65, 57M27

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