The extending surfaces of immersions into surfaces

Abstract

Blank solved the question of classifying immersed circles in R 2 that extend to immersed disks, and how many topologically inequivalent disks can be extended. The quetions of various cases in 2-dimension have already been solved by generalizing his method. In this paper, we give a new way, which is straightforward for the questions, and we determine all topological equivalence classes of immersed surfaces bounded by an arbitrary immersed circle in a closed oriented surface.