I propose an alien-geometry topic challenge.
Its often hard to tweak the mathematics of a world (for example, you can't really make 2+2=5 in a reasonable way), but one way you can is by tweaking the geometry. This can lead to many interesting implications, including chemical, biological, and even cultural implications.
Also, the use of quotient spaces helps too.
EDIT: It appears to be finished. If someone wants to propose another tag challenge, go ahead.