He does not invite Odysseus back to the island.
The cyclops was already named Polyphemus. Odysseus did not name the cyclops.
In the "Odyssey", Odysseus blinded the Cyclops Polyphemus with a red hot log.The cyclops that was blinded by Odysseus is Polyphemos.
Odysseus blinded Poseidon's son's eye who is a Cyclops. So he was cursed that can not go back home. He tried to go back home in the Odyssey.
In the cyclops cave
Cyclops asked Poseiden to add to Odysseus' fate.
He thought it was a waist of time and that it was stupid,
When Odysseus shouted back at the cyclops as he and his men were escaping, he revealed his real name, which goes against his cunning nature of using aliases. This decision ultimately led to Poseidon's anger towards him, causing further obstacles in his journey back home.
The cyclops was already named Polyphemus. Odysseus did not name the cyclops.
Odysseus expects the cyclops to bear gifts to the travelers.
Odysseus did not kill the cyclops Polyphemus.
In the "Odyssey", Odysseus blinded the Cyclops Polyphemus with a red hot log.The cyclops that was blinded by Odysseus is Polyphemos.
Odysseus blinded Poseidon's son's eye who is a Cyclops. So he was cursed that can not go back home. He tried to go back home in the Odyssey.
In the cyclops cave
Cyclops asked Poseiden to add to Odysseus' fate.
The Cyclops ate Odysseus' men.
Odysseus was curious about the type of men the Cyclops were.
Odysseus did not tell the cyclops his name cyclops promised him a gift