Unlike Finnegans Wake, to which he was indifferent, Nabokov thought Ulysses one of the greatest  novels of the twentieth century. In his dissection of the novel, when teaching at Cornell, he disdained the Homeric parallels, supplying only a map of Dublin. Quizzed about this practise in Strong Opinions Nabokov answers:

Joyce himself very soon realized with dismay that the harping on those essentially easy and vulgar “Homeric parallelisms” would only distract one’s attention from the real beauty of the book. He soon dropped these pretentious chapter titles which already were “explaining” the book to non-readers. In my lectures I tried to give factual data only.

In Lectures on Literature Nabokov goes further:

 I must especially warn against seeing in Leopold Bloom’s humdrum wanderings and minor adventures on a summer day in Dublin a close parody of the Odyssey, with the adman Bloom acting the part of Odysseus, otherwise Ulysses, man of many devices, and Bloom’s wife representing chaste Penelope while Stephen Dedalus is given the part of Telemachus. That there is a very vague and very general Homeric echo of the theme of wanderings in Bloom’s case is obvious, as the title of the novel suggests, and there are a number of classical allusions in the course of the book; but it would be a complete waste of time to look for close parallels in every chapter and every scene of the book. There is nothing more tedious than a protracted and sustained allegory based on a well-worn myth; and after the work had appeared in parts, Joyce promptly deleted the pseudo-Homeric titles of his chapters when he saw what scholarly and pseudoscholarly bores were up to.

Thankfully Steven Riddle was helpful, in commenting on an earlier post, to steer me away from worrying too much about the Homeric allusions and more toward a visit to Dublin. Very sound advice which I shall surely take.