On surface-knots with triple point number at most three

2017/11/13 by A. Al Kharusi, Kharusi, Amal Al, Tsukasa Yashiro +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algebraic Topology (math.AT) #Connective tissue disorders research #FOS: Mathematics #Geometric and Algebraic Topology #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1711.04838

openalex publication_date 2017/11/13 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that if a diagram of a surface-knot F has at most three triple points, then the cocyle invariant of F is an integer. In particular, for a surface-knot of genus one, the triple point number invariant is at least four.

Related

• The triple point number of surface-knots of genus one is at least four
• No surface-knot of genus one has triple point number two
• On the triple point number of surface-links in Yoshikawa's table
• 2-knot homology and Yoshikawa move
• A triple coproduct of curves and knots