No abstract

It is known that there is no 2-knot with triple point number two. The present paper 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.

In this paper, we prove that if a surface diagram of a surface-knot has at most two triple points and the lower decker set is connected, then the surface-knot group is isomorphic to the infinite cyclic group.

In this paper we give a lower bound of triple point numbers of special family of 2-knots colored by the dihedral quandle of order 5.

In this paper, we present a construction of a family of surface-knot diagrams with cross-exchangeable curves, along which we can change the crossing information to obtain trivial diagrams. These diagrams also satisfy a kind of minimality, called [Formula: see text]-minimal surface-knot diagrams.