THE SPUN TREFOIL NEEDS FOUR BROKEN SHEETS-Reference-Cited by-同舟云学术

THE SPUN TREFOIL NEEDS FOUR BROKEN SHEETS

Published:2005-11 Issue:07 Volume:14 Page:853-858
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

SAITO MASAHICO¹,SATOH SHIN²

Affiliation:

1. Department of Mathematics, University of South Florida, Tampa, FL 33620, USA

2. Graduate School of Science and Technology, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

Abstract

We prove that if a surface-knot diagram is colored by a specific quandle non-trivially, then any diagram of the surface-knot consists of at least four broken sheets. In particular, the minimal number of broken sheets for the spun trefoil is shown to be exactly four.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216505004123

Reference6 articles.

1. Extensions of Quandles and Cocycle Knot Invariants

2. Quandle cohomology and state-sum invariants of knotted curves and surfaces

3. GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY

4. A classifying invariant of knots, the knot quandle

5. DISTRIBUTIVE GROUPOIDS IN KNOT THEORY

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