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Consider the following example (PDFLaTeX, TeXLive 2011):

% This isn't *stricly* necessary, of course...
  \def\ensuremath#1{\TextOrMath{\(\relax #1\)}{#1}}
% Common double-struck characters such as ℂ, ℍ, ℕ, ℙ, ℚ, ℝ and ℤ are
% set up to work by inputenc.sty.  They are in the range u+2102-2149
% along with some other characters that aren't in amsmath's blackboard
% bold font such as ⅆ and ⅈ.
\defTeXorMathorUnicodePDFcmd\CC{\mathbb C}{ℂ}
% 𝔽 is an example of a character that inputenc.sty doesn't make work. 
% It - along with the characters 𝔸, 𝔹, 𝔻, &c - are in the completely 
% different range u+1D538-1D7E1.
\defTeXorMathorUnicodePDFcmd\FF{\mathbb F}{𝔽}
\begin{document} \section{\CC and \FF, [\ldots]} \end{document}

The purpose of \CC is to get ℂ in both the text and the PDF TOC when used in for example a section header. What's needed to get \FF to do the same for 𝔽 (and similarly for the other "uncommon" double-struck characters)?

PS: I copied the characters from here: http://graphemica.com/search?q=double+struck

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I can see both ℂ and 𝔽 in the bookmark, both with Skim and Adobe Reader. – egreg Feb 23 '12 at 11:59
I feel like an idiot... in my original file, I had those macro definitions before \usepackage[unicode]{hyperref}. Of course Adobe Reader doesn't display the double-struck F because its UI font is missing the glyph, but moving the definitions of \FF and friends to after hyperref did fix the problems I was having with pdflatex giving errors. – kahen Feb 23 '12 at 12:31
I don't get errors even putting the definitions before loading hyperref – egreg Feb 23 '12 at 12:39
But you made me encounter a valid problem trying to understand yours... And now I'd like to have it solved. – Frédéric Grosshans Feb 28 '12 at 18:16

This is not an proper answer, but an analysis of the problem.

The problem seems pdf-viewer dependent. I see 𝔽 in the bookmarks with Adobe Reader, but not with Evince (a Linux pdf-viewer). The error message hints at the source of the error : it says that ' \xed\xa0\xb5\xed\xb4\xbd' (for 𝔽) is not a valid UTF8 sequence. Indeed, it is not a UTF-8 byte sequence, but a CESU-8 sequence. They are indistinguishable most of the common characters (on the basic multilingual plane), but 𝔽 is on another plane.

I don't know whether the pdf-format wants UTF-8 or CESU-8 encoded text, so I don't know if the bug is on the pdf generation side (in pdflatex) or on the viewer side.

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