How can I analyze Hemingway's story "Hills Like White Elephants" using Freud's theories from Letter 52 to answer, referring to the unconscious topic of the text affecting the characters, what the omission of the topic could mean?
This complex question can get only the briefest answer in this format but it will guide you to further thought and investigation. Freud's letter to Wilhelm Fliess, dated Vienna, November 14, 1897, discusses the the concept of what later came to be translated as "afterwardness," a vague and obscure label for a concept that relates to Freud's attempt to definitively identify the mechanism of "repression."
In the original letter written in German, Freud uses the word "Nachträglichkeit," later translated as either "afterwardness" or as "deferred action," to define the concepts discussed.
A release of sexuality ... comes about ... from memory traces -- therefore also by the path of deferred action. ... [in which] the preconscious and a sense of consciousness turn away from the memory. This is repression. (Nov 14, 1897)
Freud's simply stated idea in this letter has been enlarged upon by Freud and others to suggest in essence that an action or event in a person's early years can lie dormant until later more mature years when that memory might be revived or suggested by later circumstances and that the generation of that memory might trigger a rejection--a deferred action of rejection--from the person concerned.
The way this might apply in analysis to the American man and to Jig, who omit the overt mention of the topic of Jig's debated abortion, is that Jig is having a deferred action of rejection against the memory of her intimacy with the American man since he is using that intimacy to compel her to undergo an abortion, an idea that is apparently abhorrent to her. If the idea of "repression" is taken out of context of "afterwardness" as discussed in Freud's letter, it might be said that Jig is willing to "repress" her feelings of repulsion to abortion in order to placate the American man.
It seems though, that these analyses might be misapplying the concepts as Freud discussed them in his letter to Fliess since Freud makes it clear in the letter that his idea applies to two stages of life: the early physiologically immature years where an incident occurs and the later physiologically mature years when the deferred reaction/rejection/repression of the early memory occurs.