Doesn't look like there is one (unless it's built into the ceiling and completely out of the frame in this shot). Unfortunately, there are MANY kitchens without ventilation, which makes a big difference in air quality.

Besides the immediate benefit of removing grease & smoke, range hoods have several other "bonuses" - check out this article for more info: http://www.futurofuturo.com/rangehood-FAQ-10-reasons-to-have-a-range-hood.php

The cooktop is equipped with downdraft vent.