In "A Rose for Emily" by William Faulkner, we cannot chart the exposition, climax and resolution as we might with another story—one that has been told in chronological order. In fact, one of the ways that Faulkner keeps the reader so off balance and able to surprise us so well at the story's end is by telling the story in several parts that are not chronologically ordered.
For instance, had the narrator told us that Miss Emily was seen riding with Homer Barron, that she then bought a silver-backed man's "toilet set" engraved with his initials, and finally purchased rat poison, we would not have been too surprised by the ending; we most probably would have remembered Homer being admitted one night by Tobe, the manservant, never to be seen again. However, by mixing things up with flashbacks—"misdirection" by the author—we have lost the chronology. There is really no resolution to the plot, as happens with some short stories; what grabs us, however, is not just that Miss Emily murdered Homer, but that the details point to evidence that she has been sleeping next to his dead body…and not many years in the past, but recently, as shown by the hair on the pillow next to the body: the color and length of her aged hair:
…we saw a long strand of iron-gray hair.
And this is not only the climax of the story, but the end of the story as well.
Because "A Rose for Emily" does not follow a normal, linear time frame--instead using several long flashbacks--it is a bit more difficult to distinguish the different stages of the short story. The narrative starts with the death of Miss Emily, before reverting back to an earlier tale of her dealings with her father's taxes. Part II continues the exposition, using a flashback to two years earlier concerning "the smell" coming from the house. Part III is yet another flashback (although it is not immediately recognized) which introduces the arrival of Homer Barron. Part IV continues the story of Homer and his disappearance, and again picking up the story from "the smell." From that point, the narrative continues in a sequential manner, charting the final years of Emily's life. Part V continues from where the story began, concluding with the breaking down of the bedroom door and the final, climactic, double surprise ending.
It is clear that the climax comes at the very end of the story; the resolution is less clear, but it would be the two sections that concern Homer and his departure, followed by "the smell."