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THE SPUN TREFOIL NEEDS FOUR BROKEN SHEETS

MASAHICO SAITO

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

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and

SHIN SATOH

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

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https://doi.org/10.1142/S0218216505004123Cited by:8 (Source: Crossref)

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.

Keywords:

AMSC: 57Q45

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