曲面の分類定理のZIP証明とその安定写像への応用について

Abstract

The aim of this article, based on the master's thesis [13] written by the first-named author, is two-fold: to provide a detailed account in Japanese of Conway's ZIP proof of the classification theorem of closed surfaces and to discuss its application to a study of stable maps. For the former purpose, we heavily rely upon the survey article [1] by George K. Francis and Jeffrey R. Weeks. The latter enables us to explicitly construct a stable map from a closed surface to the plane with any number of cusp points satisfying the Whitney-Thom congruence formula.