Notations involving squiggly lines over horizontal lines Is there a symbol for "homeomorphic to"? I looked on Wikipedia, but it doesn't seem to mention one? Also, for isomorphism, is the symbol a squiggly line over an equals sign? What is the symbol with a squiggly line over just one horizontal line? Thanks. 

I agree with Qiaochu Yuan's answer for the most part, but if you are working in an area where you must distinguish between homeomorphism, homotopy equivalence, and diffeomorphism, the standard notation becomes ambiguous.  This has been relevant for me because I've been studying the interplay of topology and geometry for hyperbolic 3-manifolds.  In this context what seems to be the most consistent is $\sim$ for homotopy equivalence, $\simeq$ for homeomorphic, and $\approx$ for diffeomorphic.  This way $\sim$ agrees with usage as indicating same members of an equivalence class, where the equivalence class is that of the fundamental group; and $\approx$ agrees with what geometers like (for instance John Lee), and $\simeq$ is just a decent choice for something that looks halfway between them.
