Name Akiko Shima Tokai University Session Jan 10 13:00~13:40 E11-102 Linear 4-charts with four crossings (joint work with Teruo Nagase) A chart is an oriented labeled graph in a disk with three kind of vertices called black vertices, crossings and white vertices. A chart represents an embedded surface in 4-space. We would like to research about embedded surfaces using charts. Let $\Gamma$ be a 4-chart, and $\Gamma_m$ the subgraph consisting of all edges of label $m$ and their vertices. Let $Cr(\Gamma)$ be the set of all crossings in $\Gamma$. If $(\Gamma_1\cup \Gamma_3)-Cr(\Gamma)$ consists of a disjoint union of trees, then $\Gamma$ is called a linear chart. We show that there does not exist any linear 4-minimal 4-chart with four crossings. 102-1-10/FourCrossingKorea.pdf