Dried-up river that flows under Hangman's Span at the foot of Friar's Keep in Marcuria. It appears to bisect the city in a North-South direction, once flowing into the Great Sea.
When Crow is reunited with April in the Dark People's Library, she suggests that the 8 years since she abandoned him are "water under the bridge". Crow replies "No. No, no, no. The Red River under Hangman's Span, that's water under the bridge." Either the river has dried up in the intervening period unbeknownst to Crow or, more likely, he is being facetious.
This may also be the Marcurian river referred to by the Map Merchant in The Longest Journey. According to him there's just bridges and a riverbed - when April asks if the river dried up, he explains "No, the river just disappeared five hundred years ago. No one knows what happened to it."