Technically it's a diaeresis, not an umlaut. It indicates the syllable break in the word "cooperate". It's not a common thing in written English, but the New Yorker has a certain writing style that calls for that sort of thing.

You're not joking, here's an extract from the Wikipedia entry [1]:

"Nowadays in English, the diaeresis is normally left out (cooperate), except by The New Yorker, or a hyphen is used (co-operate). It is, however, still common in loanwords such as naïve and Noël."

This made me smile. Thanks! :)

[1] http://en.wikipedia.org/wiki/Hiatus_(linguistics)

It's pretty deeply preferable to "co-operating," if you ask me.

philwelch is right on, but to give a less technical explanation, it's a signal to pronounce the world (co)(operating) instead of (coop)(erating).

The New Yorker does it for all doubled vowels that aren't pronounced as long vowels.