No surface-knot of genus one has triple point number two

2015/06/04 by Kharusi, A. Al, Yashiro, T.
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1506.01489

Abstract

It is known that there is no 2-knot with triple point number two. The present work shows that there is no surface-knot of genus one with triple point number two. In order to prove the result, we use Roseman moves and the algebraic intersection number of simple closed curves in the double decker set.

Related

• The triple point number of surface-knots of genus one is at least four
• On surface-knots with triple point number at most three
• 2-knot homology and Roseman move
• A TABLE OF GENUS TWO HANDLEBODY-KNOTS UP TO SIX CROSSINGS
• On the triple point number of surface-links in Yoshikawa's table