The symbol for a map which is an isomorphism?

Question

Suppose I have a map A → B which is an isomorphism. I'd like to represent this as something that looks like \rightarrow with \simunder it. I could try \underset{}_{}, but is there already a ready made symbol?

I couldn't find the symbol using Detexify, nor in the comprehensive list of LaTeX symbols.

Answer 1

Theoretically, you could use \xrightarrow[\sim]{} (from amsmath) or \xlongrightarrow[\sim]{} (from extarrows). Both look horrible though. The \sim on top of the arrow (like \xlongrightarrow{\sim}) looks somewhat better.

Unicode defines ⥴ (U+2974 RIGHTWARDS ARROW ABOVE TILDE OPERATOR), which you can use in case you run Xe/LuaLaTeX with unicode-math (either directly or with the \rightarrowsimilar alias). There are also ⥱ (\equalrightarrow), ⥲ (\similarrightarrow), ⥳ (\leftarrowsimilar), ⥵ (\rightarrowapprox) and other strange things.

Answer 2

A bit of adjustment of the spacing may help. For example, with

\documentclass{article}
\usepackage{amsmath,fixltx2e}
\newcommand*\MapsTo{%
  \xrightarrow[\raisebox{0.25 em}{\smash{\ensuremath{\sim}}}]{}%
}
\begin{document}
Test \( x \MapsTo y \) test.
\end{document}

I feel the result is not tool bad. You may need to adjust the amount of vertical shift to suite the font in use. I've not scaled-down the \sim here, as it's not clear from the original question if it should be full-sized or small. It would be easy enough to do that, though, if necessary.