This is a reference to the Greek myth of the Twelve Labors of Hercules (the Roman form of the Greek demigod Heracles). The Fifth Labor was to clean the Augean Stables in one day. The Labors were tasks to be performed by Hercules as penance. Cleaning the stables of King Augeas (one of Jason’s Argonauts) was supposed to be both humiliating and impossible, since the cattle were immortal and produced an incredible amount of manure.
However, Heracles didn’t use a broom. He got around the challenge of the job by diverting the two rivers Alpheus and Peneus through the stables. It is odd that Kundera would choose the image of “Hercules’ broom” since there wasn’t one and he surely would know that, but perhaps this is meant to suggest the indistinctness and outright inaccuracy of Franz’s romantic notions.
This gilded bronze Roman statue of Hercules with the apples of the Hesperides dates from the 2nd century BCE and currently resides in the Capitoline Museums in Rome.