Can there be surface convergence associated with an upper level high?

[Brewers]

Considering high pressure at the 500 mb height field, where the geostrophic wind at the surface, which is flat, is calm. Also neglect friction, diabatic heating and water vapor. Can there be surface convergence?

[isohume]

Yes, it happens all the time with thermal lows, lee trofs, etc.

It's not rare for the atmosphere to be non-classical in nature...there are always varying forces of different scales working constructively and destructively in any given pattern.