This is a workshop of KSS Projects for Communication: Low Dimensional Topology and Computer Graphics, and we would like to have a deep discussion on the topic hence attendance is limited to only the related colleagues who have been contacted with us in advance. If you are a specialist in this topic and interested in our workshop, please contact to the corresponding organizer: Kosaku Nagasaka in advance.
We discuss the method of examing surfaces and their deformations by using the neighborhood of the contours.
A short summary of my implementation that I had contributed for Studio Phones Fellowship Program, as an introduction.
Suppose that an immersion of oriented circles to the plane is given. There is a problem when this immersion extends to an immersion of a surface to the plane. In 1967, Blank gave a necessary and sufficient condition when an immersed circle extends to an immersed disk. After that, in 1976, Francis solved this problem by extending Blank’s methd. In this talk, the speaker will introduce Francis' work. If there is time, the speaker will introduce Francis-Troyer’s method (1977)determining whether plane curves with cusps can be realized as a contour of a stable map of a closed surface to the plane.