Although this word was made up in order to be a contender for the longest word in English, it can be broken down into smaller chunks in order to understand it.
Anti- means that you are against something; monopoly means the exclusive control over something; geographic is related to geography; and the remaining part has to do with nationalism.
So this word means something like 'a nationalistic feeling of being against geographic monopoly,' but you can see that it doesn't have much sense.
Transverse is to stretch across something
The dictionary definition is
situated or extending across something."a transverse beam supports the dashboard"<span>synonyms:<span>crosswise, crossways, cross, horizontal, diagonal, oblique, slanted</span></span>
