The structure of a minimal n-chart with two crossings I: Complementary domains of Γ1 ∪ Γn−1

Abstract

This is the first step of the two steps to enumerate the minimal charts with two crossings. For a label [Formula: see text] of a chart [Formula: see text] we denote by [Formula: see text] the union of all the edges of label [Formula: see text] and their vertices. For a minimal chart [Formula: see text] with exactly two crossings, we can show that the two crossings are contained in [Formula: see text] for some labels [Formula: see text]. In this paper, we study the structure of a disk [Formula: see text] not containing any crossing but satisfying [Formula: see text].