Properties of minimal charts and their applications XI: no minimal charts with exactly seven white vertices

Abstract

Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface embedded in 4-space. In this paper, we investigate embedded surfaces in 4-space by using charts. In this paper, we shall show that there is no minimal chart with exactly seven white vertices.