\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\pp@spagectr{FN@totalid}{1}{1}{1}
\pp@spagectr{FN@totalid}{2}{1}{1}
\pp@spagectr{FN@totalid}{3}{1}{1}
\pp@spagectr{FN@totalid}{4}{1}{1}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}}
\citation{Ohtsuki:QuantumInvariants}
\newlabel{ssec:Reminder}{{1.1}{2}{A Quick Reminder of Algebras and R-matrices}{subsection.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{A Quick Reminder of Algebras and R-matrices}}{2}{subsection.1.1}}
\@writefile{brf}{\backcite{Ohtsuki:QuantumInvariants}{{2}{1.1}{subsection.1.1}}}
\@writefile{loAside}{\contentsline {Aside}{\numberline {1.1}{\ignorespaces The standard methodology on an example knot.\relax }}{2}{Aside.caption.2}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{aside:URCMethod}{{1.1}{2}{The standard methodology on an example knot.\relax }{Aside.caption.2}{}}
\citation{KBH}
\pp@spagectr{FN@totalid}{5}{1}{3}
\newlabel{ssec:AbstractExpanded}{{1.2}{3}{An Expansion of the Abstract}{subsection.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{An Expansion of the Abstract}}{3}{subsection.1.2}}
\newlabel{ssec:Plan}{{1.3}{3}{Plan of the paper}{subsection.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Plan of the paper.}}{3}{subsection.1.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Acknowledgement}}{3}{subsection.1.4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Rotational Virtual Tangles}}{3}{section.2}}
\newlabel{sec:RVK}{{2}{3}{Rotational Virtual Tangles}{section.2}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Meta-Hopf Algebras and the Drinfel'd Double Construction}}{3}{section.3}}
\@writefile{loAside}{\contentsline {Aside}{\numberline {3.1}{\ignorespaces Ordinary Hopf Algebras.\relax }}{3}{Aside.caption.3}}
\newlabel{aside:OrdinaryHopf}{{3.1}{3}{Ordinary Hopf Algebras.\relax }{Aside.caption.3}{}}
\pp@spagectr{FN@totalid}{6}{1}{4}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Meta-monoids vs.\ monoid objectss in a monoidal category}}{4}{subsection.3.1}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The Category of Perturbed Gaussian Differential Operators}}{4}{section.4}}
\@writefile{brf}{\backcite{KBH}{{4}{\leavevmode {\color  {green!50!black}2}}{Aside.caption.3}}}
\bibcite{KBH}{BN}
\bibcite{InonuWigner:ContractionOfGroups}{IW}
\bibcite{Kauffman:RotationalVirtualKnots}{Ka}
\bibcite{Ohtsuki:QuantumInvariants}{Oh}
\bibcite{Overbay:Thesis}{Ov}
\bibcite{Rozansky:Flat1}{Ro1}
\bibcite{Rozansky:Burau}{Ro2}
\bibcite{Rozansky:U1RCC}{Ro3}
\bibcite{Wolfram:Mathematica}{Wo}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{68.86317pt}
\newlabel{tocindent1}{77.67142pt}
\newlabel{tocindent2}{34.5pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Solavble Approximations of Semi-Simple Lie Algebras}}{5}{section.5}}
\newlabel{sec:SolvApp}{{5}{5}{Solavble Approximations of Semi-Simple Lie Algebras}{section.5}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Odds and Ends}}{5}{section.6}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{A}{Tables}}{5}{appendix.A}}
\newlabel{app:Tables}{{A}{5}{Tables}{appendix.A}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{}{References}}{5}{section*.4}}
\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\pp@spagectr{FN@totalid}{1}{1}{1}
\pp@spagectr{FN@totalid}{2}{1}{1}
\pp@spagectr{FN@totalid}{3}{1}{1}
\pp@spagectr{FN@totalid}{4}{1}{1}
\citation{Ohtsuki:QuantumInvariants}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{3}{section.1}}
\newlabel{ssec:Reminder}{{1.1}{3}{A Quick Reminder of Algebras and R-matrices}{subsection.1.1}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{A Quick Reminder of Algebras and R-matrices}}{3}{subsection.1.1}}
\@writefile{brf}{\backcite{Ohtsuki:QuantumInvariants}{{3}{1.1}{subsection.1.1}}}
\@writefile{loAside}{\contentsline {Aside}{\numberline {1.1}{\ignorespaces The standard methodology on an example knot.\relax }}{3}{Aside.caption.2}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{aside:URCMethod}{{1.1}{3}{The standard methodology on an example knot.\relax }{Aside.caption.2}{}}
\pp@spagectr{FN@totalid}{5}{1}{4}
\newlabel{ssec:AbstractExpanded}{{1.2}{4}{An Expansion of the Abstract}{subsection.1.2}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{An Expansion of the Abstract}}{4}{subsection.1.2}}
\newlabel{ssec:Plan}{{1.3}{4}{Plan of the paper}{subsection.1.3}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Plan of the paper.}}{4}{subsection.1.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Acknowledgement}}{4}{subsection.1.4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Rotational Virtual Tangles}}{5}{section.2}}
\newlabel{sec:RVK}{{2}{5}{Rotational Virtual Tangles}{section.2}{}}
\citation{KBH}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Meta-Hopf Algebras and the Drinfel'd Double Construction}}{7}{section.3}}
\pp@spagectr{FN@totalid}{6}{1}{7}
\@writefile{brf}{\backcite{KBH}{{7}{\leavevmode {\color  {green!50!black}2}}{Aside.caption.3}}}
\@writefile{loAside}{\contentsline {Aside}{\numberline {3.1}{\ignorespaces Ordinary Hopf Algebras.\relax }}{7}{Aside.caption.3}}
\newlabel{aside:OrdinaryHopf}{{3.1}{7}{Ordinary Hopf Algebras.\relax }{Aside.caption.3}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Meta-monoids vs.\ monoid objectss in a monoidal category}}{8}{subsection.3.1}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The Category of Perturbed Gaussian Differential Operators}}{9}{section.4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Solavble Approximations of Semi-Simple Lie Algebras}}{11}{section.5}}
\newlabel{sec:SolvApp}{{5}{11}{Solavble Approximations of Semi-Simple Lie Algebras}{section.5}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Odds and Ends}}{13}{section.6}}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{A}{Tables}}{13}{appendix.A}}
\newlabel{app:Tables}{{A}{13}{Tables}{appendix.A}{}}
\bibcite{KBH}{BN}
\bibcite{InonuWigner:ContractionOfGroups}{IW}
\bibcite{Kauffman:RotationalVirtualKnots}{Ka}
\bibcite{Ohtsuki:QuantumInvariants}{Oh}
\bibcite{Overbay:Thesis}{Ov}
\bibcite{Rozansky:Flat1}{Ro1}
\bibcite{Rozansky:Burau}{Ro2}
\bibcite{Rozansky:U1RCC}{Ro3}
\bibcite{Wolfram:Mathematica}{Wo}
\@writefile{toc}{\contentsline {section}{\tocsection {Appendix}{}{References}}{15}{section*.4}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{68.86317pt}
\newlabel{tocindent1}{77.67142pt}
\newlabel{tocindent2}{34.5pt}
\newlabel{tocindent3}{0pt}
