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\usepackage[setpagesize=false]{hyperref}

\def\sheeturl{{\url{http://drorbn.net/AcademicPensieve/2013-10/}}}
\def\calK{{\mathcal K}}
\def\calA{{\mathcal A}}
\def\wTF{{\mathit w\!T\!F}}
\def\wTFe{{\widetilde{\mathit w\!T\!F}}}
\def\sKTG{{\mathit s\!K\!T\!G}}


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\newcommand{\cheatline}{\vskip 1mm\refstepcounter{linecounter}\thelinecounter. }
% Following http://tex.stackexchange.com/questions/23521/tabular-vertical-alignment-to-top:
\def\imagetop#1{\vtop{\null\hbox{#1}}}

\def\arXiv#1{{\href{http://front.math.ucdavis.edu/#1}{arXiv:#1}}}
\def\qed{{\hfill\text{$\Box$}}}

\def\bbR{{\mathbb R}}
\def\bbZ{{\mathbb Z}}
\def\RP{\bbR{\mathrm P}}

\begin{document}
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\parbox[b]{3.25in}{
  {\LARGE\bf Cheat Sheet Double Tree}
  \newline \footnotesize Joint with Zsuzsanna Dancso.
}
\hfill\parbox[b]{4.75in}{\small
  \null\hfill\sheeturl
  \newline\null\hfill initiated 16/10/13;
    modified \today, \ampmtime
}

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\begin{multicols}{2}
Let $\calK^{uw}$ be the algebraic structure $[\sKTG \stackrel{a}{\rightarrow} \wTFe]$, where $\sKTG$ is signed knotted trivalent $(1,1)$-tangles.
$\wTFe$ is $\wTF^o$ with added generators $\left\{\raisebox{-2mm}{\input{AddedGens.pstex_t}}\right\}$ now a coloured circuit algebra. All Reidemeister
and OC relations appear with all possible colourings. Two? new operations: ori switch of red strands and puncture of black.  
The projectivization of $\calK^{uw}$ is $\calA^{uw}=[\calA^u \stackrel{\alpha}{\rightarrow} \calA^{sw}]$, where in $\calA^{sw}$ 1-wheels are zero
and so are tails on red strands.

{\bf Theorem 0.}
$\exists$ homomorphic expansion $Z^{uw}=(Z^u,Z^w)$ for $\calK^{uw}$. (In particular $\alpha Z^u=Z^w a$.)

\end{multicols}

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\input CSDT-Dror.tex

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