The rebels' map of Britain in Act 3, Scene 1 seems particularly relevant. Here, we want to argue that the map points to 1) Hotspur's incompetence as a leader and 2) the general threat his rebellion poses to the kingdom. As the rebels prepare to talk strategy, Hotspur shouts "a plague upon it! / I have forgot the map" (3.1.1). Uh oh. Glendower finds it, of course, but we're immediately struck by Hotspur's disorganization and seeming ineptitude. Hello. If the guy can't even keep track of his map, how's he supposed to pull off a rebellion and lead the country if he succeeds in deposing King Henry? In this moment, the map seems to be symbolic of the kingdom as a whole and gestures toward Hotspur's inability to manage Britain.
When Hotspur unfurls his map (after Glendower finds it for him, of course) and demonstrates how the rebels plan to divide the kingdom into three parts, we're reminded that the rebel cause is bent on division and dissection, not unity. The business with the map seems to confirm that young Percy's plans are decidedly not in the best interest of a kingdom that's moving toward unification. (This is sort of the same problem in King Lear. When Lear retires and divides his kingdom into three parts, it spells disaster with a capital D.)
Check out this picture of Queen Elizabeth I, a colonial monarch, with her feet planted atop a world globe. At the time Shakespeare wrote Henry IV Part 1 (around 1597), England was very much concerned with the unification of Britain and global expansion in general. In Shakespeare's day, maps and globes were often used as symbols of England's status as a big, giant world power, not a kingdom that's been hacked up into little bits and pieces.
In Engendering a Nation, influential literary critics Jean E. Howard and Phyllis Rackin argue that "the rebel cause is discredited, not only or even chiefly because it defies the authority of the monarch, but because it threatens to dismember the body of the land, a threat that is graphically illustrated when the rebel leaders haggle over the map of Britain and agree finally to have the river Trent turned from its natural course in the interest of their 'bargain'" (162-163). It's no surprise, we would add, that, when Mortimer complains about the rebels' division of the kingdom, he says the land has been "gelded" (a common term for castration). See our discussion of "Body Mutilation" above."