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- Title
Amphicheirality of ribbon 2-knots.
- Authors
Yasuda, Tomoyuki
- Abstract
For any classical knot k 1 , we can construct a ribbon 2 -knot spun (k 1) by spinning an arc removed a small segment from k 1 about R 2 in R 4 . A ribbon 2 -knot is an embedded 2 -sphere in R 4 . If k 1 has an n -crossing presentation, by spinning this, we can naturally construct a ribbon presentation with n ribbon crossings for spun (k 1). Thus, we can define naturally a notion on ribbon 2 -knots corresponding to the crossing number on classical knots. It is called the ribbon crossing number. On classical knots, it was a long-standing conjecture that any odd crossing classical knot is not amphicheiral. In this paper, we show that for any odd integer n there exists an amphicheiral ribbon 2 -knot with the ribbon crossing number n.
- Subjects
KNOT theory; INTEGERS; LOGICAL prediction
- Publication
Journal of Knot Theory & Its Ramifications, 2020, Vol 29, Issue 9, pN.PAG
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216520500698