On a banded link presentation of knotted surfaces

Abstract

We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we will investigate surface-knot with one critical point of index 1. Then we show infinitely many mutually distinct surface-knots that has an embedding with two critical points of index 1. Next we define a long flat for a banded link for any surface-knot and show diagrammatically a long flat form of $n$-twist-spun $(2,t)$-torus knots.

Cited by in corpus (6)

• Minimal hard surface-unlink and classical unlink diagrams
• Independence of Yoshikawa eighth move and a minimal generating set of band moves
• Distances between surfaces in 4-manifolds
• Shadows of 2-knots and complexity
• Flattening knotted surfaces
• Minimal generating set of planar moves for surfaces embedded in the four-space