How can I remove thick dust on the top of a wardrobe?
Cover entire top of wardrobe with king sized bed sheet.  Lay it down gently across the top, right on the dust.  Don't stir it up.
Scoot edges in along the top of wardrobe, pushing dust in front of them.  Dust pushed into the air will remain trapped under the sheet.
When you have pushed edges in to center, dust will be inside sheet.  Gather edges in the middle of the wardrobe and take sheet (now bag) outside to shake dust out.  
Bring sheet back in and use it to wipe off residual dust.  Take back outside to shake.
Bring sheet back in and use furniture polish and sheet to clean wardrobe top.  


would it be too much to ask that you post a picture of the dust?  Prurient interest, perhaps, but I want to see dust that thick.