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.

41 pages, 36 figures, this paper is the last in this series