I have thought about spheres in higher dimensions for  along time--that is the subject called homotopy but never came to any new ideas there except that the more symmetries you have in higher dimensions the less fields should be available which would limit any worlds there. So you can see why a world like in String Theory with 10 dimensions should still be limited to 3 space and one time just to have a place to have interesting results. Knots is a good example where adding dimensions makes a place where you can not have knots . They can slip.