Non-slice 3-stranded pretzel knots-Reference-Cited by-同舟云学术

Non-slice 3-stranded pretzel knots

Published:2022-03 Issue:03 Volume:31 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Kim Min Hoon¹²³,Lee Changhee¹²³,Song Minkyoung¹²³^ORCID

Affiliation:

1. Department of Mathematics Education, Kyungpook National University, Daegu, 41566, Republic of Korea

2. Department of Mathematics, POSTECH, Pohang Gyeongbuk 37673, Republic of Korea

3. Center for Research in Topology, POSTECH, Pohang Gyeongbuk 37673, Republic of Korea

Abstract

Greene-Jabuka and Lecuona confirmed the slice-ribbon conjecture for 3-stranded pretzel knots except for an infinite family [Formula: see text], where [Formula: see text] is an odd integer greater than [Formula: see text]. Lecuona and Miller showed that [Formula: see text] are not slice unless [Formula: see text]. In this note, we show that four-fifths of the remaining knots in the family are not slice.

Funder

National Research Foundation of Korea

Institute for Basic Science

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216522500183

Reference11 articles.

1. Pretzel links, mutation, and the slice-ribbon conjecture

2. Slice implies mutant ribbon for odd 5–stranded pretzel knots

3. The slice-ribbon conjecture for 3-stranded pretzel knots

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