Answer:
Based on these definitions I searched, I would go with aspersion since the guy's reputation would fall.
Explanation:
aspersion: an attack on the reputation or integrity of someone or something.
abnegation: the act of renouncing or rejecting something.
approbation: approval or praise.
aberration: a departure from what is normal, usual, or expected, typically one that is unwelcome.
arrogation: to claim or seize without justification
On is the only preposition in this sentence. A preposition shows location, such as, on, over, beside, etc.
It's important because the ancient Greeks traveled. And, an odyssey is like a wonder, and if your a Greek and you liked to journey, you'd probably like to go to places with odysseys in them
Changed is the another word or synonym for wavered