Part of this is going to come from your own impressions of Jig and the American. When developing any type of thesis, much of it comes from what you think you are able to prove in the process. I think that you could argue that both of them represent the "Lost Generation" components of the Post World War I time period. This might start off very basic, but there are some significant points to be made in this process. Although there are several arguments against it, some have made the argument that the American is Hemingway, himself. This might be something to investigate, as well. If you have some understanding in how women have been portrayed in other Hemingway works, you could compare Jig to these women in attempting to paint a portrait of how women are shown in Hemingway's writings. I think that much of this is going to hang on what you take away from the text and how you see both characters. Once this is established in a way that makes sense to you and your relationship to the story, I think that constructing a thesis can transpire.