Simple Morse Functions on an Oriented Surface with Boundary

摘要

In the paper, smooth functions with non-degenerate critical points ona smooth compact surface with boundary are considered. Firstly, it isshown that these functions are topologically equivalent to m-functions. Theequipped Reeb graph is used to describe their topological structure. Secondly,the authors characterize the topological structure of all simple functionswith at most 5 critical points. And finally, a formula for the genus ofthe surface based on the equipped Reeb graph is obtained.