Is the air that travels over the wing of the plane is more dense?

A wing when looked upon from the wing tip is curved at the top and straight along the bottom. So, now there is more surface area on the top in comparison to the bottom. As air rushes along on both sides the air on the bottom is less dense and has a higher pressure compared to the air along the top. Think of the air on top as "stretched out" and therefore thinner than the air on the bottom. This creates a low pressure allowing the high pressure air on the bottom to push up. Ergo, flight.