Accepting European math postdoc offers and leaving after a year
Going for one year would fulfill your obligations as I understand them, but I can't guarantee the PI will see things the same way.  You should discuss it as soon as possible, to settle the issue and so the PI can at least make realistic plans.  (I'd be a little offended if I discovered that someone visiting to work with me had dramatically changed their plans without telling me until much later, even if I thought the change was otherwise reasonable.)

There are several plausible outcomes:


The PI might insist that you have made a commitment to stay for more than a year.  I don't think this is reasonable or likely, but it's better to find out now than later, so you can figure out what to do about it.
The PI might be fine with one year.  Then you won't have to worry about this issue any further.
The PI might accept one year but seem unhappy about it.  In that case, you could explain that you would really like to come for a year if possible, but you would be willing to withdraw if the PI would prefer to hire someone else for the full three years.