What is a good topic in the Odyssey to write an eight-page research paper on?

For a research paper, you can try discussing certain themes from The Odyssey. I will discuss two below.

1) Hospitality

This is one of the major themes of the story. Some questions to explore:

a) Should hospitality be regarded as a reciprocal arrangement?

b) If guests abuse their privilege, what recourse does the host have?

c) If the host in question is powerless to prevent her quests from taking further unwanted liberties with her person and property, should she resort to violence? If she cannot do so, should another party resort to violence on her behalf?

In the story, Odysseus' wife, Penelope, is powerless against the machinations of her suitors. They shamelessly consume food and drink at Odysseus and Penelope's expense, and they also appropriate every luxury in the couple's palace for their own. Here, you can refer to the text to help you provide examples for the suitors' despicable conduct.

With Odysseus missing and Telemachus weakened by his fear, Penelope is forced to repress her anger. Instead, she uses her wits to keep her suitors at bay. She resorts to trickery by telling them that she must finish Laertes' shroud before she can marry any of them. Each night, she unravels her work so that the shroud is never completed. For three years, she manages to trick her suitors with her story. Later, when she senses that Odysseus is nearby (in the guise of the beggar), Penelope becomes more confident. She proclaims that she will only marry the suitor who can wield Odysseus' bow successfully.

Of course, the beggar (being Odysseus) is the only one who can truly wield his bow. Upon being exposed as Odysseus himself, the long-suffering husband proceeds to slaughter all of Penelope's suitors. Now, the denouement raises interesting questions. The suitors' relatives demand restitution for the deaths. Are their claims valid? Is Halitherses' proclamation that the suitors received their just deserts a good argument? Essentially, we revisit the question of whether hospitality should be a reciprocal arrangement. Your answer to this can be used as a working thesis statement for your essay.

2) Loyalty/ Fidelity.

Loyalty is a main theme in The Odyssey, and in Penelope's case, loyalty is richly rewarded. In the story, servants who remain loyal are also presented in a positive light. Some questions to consider regarding this theme:

1) Does gender play a role in defining loyalty? How does Penelope's loyalty differ from her husband's conception of marital fidelity?

Compare and contrast Penelope's sexual fidelity and Odysseus' seemingly gratuitous sexual indulgence while he is away. At the same time, it can be said that Odysseus is loyal in his own way: he overcomes great odds to return home to his wife and son. Is it possible to reconcile the two differing standards of loyalty? 

2) How do loyal servants preserve familial integrity? In The Odyssey, Eurykleia is a minor character, but her influential position helps her convince Telemachus to stay with Penelope. When Odysseus returns, she is one of the original few who recognizes him through his disguise. For more information about this, please refer to Book 19.

Basically, you can discuss how Homer uses the differing types of loyalty to tell an engaging story and to provide a glimpse into ancient attitudes about love, family, and community.