A glome is a 4 dimensional sphere, the hypersphere version of a tesseract, a hypercube.
Five men are herding fifteen horses down the road. They won't be very talkative, but are willing to sell a horse, or more horses if the heroes are interested. These men are horse thieves. They are already sought by regional militiamen. Anyone with a stolen horse (all are marked) may get into trouble. If found guilty, horse thieves face prison or even a hanging execution. Similar thefts have happened only a month before, and a reward is offered.