\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]{}
\citation{Alexander:TopologicalInvariants}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\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{brf}{\backcite{Alexander:TopologicalInvariants}{{1}{(document)}{Doc-Start}}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}}
\@writefile{brf}{\backcite{Self}{{1}{}{Doc-Start}}}
\citation{Alexander:TopologicalInvariants}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces  A demo program computing $z_1$, some initial data, and a sample run on the 0-framed trefoil knot. The program is written in {\sl  Mathematica}\nonbreakingspace \cite  {Wolfram:Mathematica} and is available at\nonbreakingspace \cite  {Self}. \relax }}{2}{figure.caption.2}}
\@writefile{brf}{\backcite{Wolfram:Mathematica}{{2}{1.1}{figure.caption.2}}}
\@writefile{brf}{\backcite{Self}{{2}{1.1}{figure.caption.2}}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:Splash}{{1.1}{2}{A demo program computing $z_1$, some initial data, and a sample run on the 0-framed trefoil knot. The program is written in {\sl Mathematica}~\cite {Wolfram:Mathematica} and is available at~\cite {Self}. \relax }{figure.caption.2}{}}
\@writefile{brf}{\backcite{Alexander:TopologicalInvariants}{{2}{1}{theorem.1.1}}}
\citation{Bar-NatanSelmani:MetaMonoids}
\citation{KBH}
\citation{Halacheva:Thesis}
\citation{Archibald:Thesis}
\citation{LeDimet:Gassner}
\citation{KirkLivingstonWang:Gassner}
\citation{CimasoniTuraev:LagrangianRepresentation}
\citation{CimasoniConway:BurauAlexander}
\citation{Wolfram:Mathematica}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\@writefile{brf}{\backcite{Bar-NatanSelmani:MetaMonoids, KBH}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{Halacheva:Thesis}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{Archibald:Thesis}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{LeDimet:Gassner, KirkLivingstonWang:Gassner, CimasoniTuraev:LagrangianRepresentation, CimasoniConway:BurauAlexander}{{3}{1}{theorem.1.1}}}
\pp@spagectr{FN@totalid}{5}{1}{3}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Algebras, Yang-Baxter Elements and Spinners, Invariants}}{3}{section.2}}
\newlabel{sec:generalities}{{2}{3}{Algebras, Yang-Baxter Elements and Spinners, Invariants}{section.2}{}}
\bibcite{Alexander:TopologicalInvariants}{Al}
\bibcite{Archibald:Thesis}{Ar}
\bibcite{Bar-Natan:OnVassiliev}{BN1}
\bibcite{KBH}{BN2}
\bibcite{Bar-NatanSelmani:MetaMonoids}{BNS}
\bibcite{Self}{BNVDV}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces  A demo program computing $z_0$, some initial data, and a sample run on the knot $8_{17}$. The program is written in {\sl  Mathematica}\nonbreakingspace \cite  {Wolfram:Mathematica} and is available at\nonbreakingspace \cite  {Self}. \relax }}{4}{figure.caption.3}}
\@writefile{brf}{\backcite{Wolfram:Mathematica}{{4}{3.1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Self}{{4}{3.1}{figure.caption.3}}}
\newlabel{fig:Splash0}{{3.1}{4}{A demo program computing $z_0$, some initial data, and a sample run on the knot $8_{17}$. The program is written in {\sl Mathematica}~\cite {Wolfram:Mathematica} and is available at~\cite {Self}. \relax }{figure.caption.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{The Lie Algebra ${\mathfrak  g}_0$, the Invariant $z_0$, and the Alexander Polynomial}}{4}{section.3}}
\newlabel{sec:g0}{{3}{4}{The Lie Algebra $\frakg _0$, the Invariant $z_0$, and the Alexander Polynomial}{section.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The Lie Algebra ${\mathfrak  g}_1$ and the Invariant $z_1$}}{4}{section.4}}
\newlabel{sec:g1}{{4}{4}{The Lie Algebra $\frakg _1$ and the Invariant $z_1$}{section.4}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Computing $z_1$}}{4}{section.5}}
\newlabel{sec:z1}{{5}{4}{Computing $z_1$}{section.5}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{An Aside on Ribbon Knots}}{4}{section.6}}
\newlabel{sec:ribbon}{{6}{4}{An Aside on Ribbon Knots}{section.6}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Questions}}{4}{section.7}}
\newlabel{sec:questions}{{7}{4}{Questions}{section.7}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{section*.4}}
\bibcite{CimasoniConway:BurauAlexander}{CC}
\bibcite{CimasoniTuraev:LagrangianRepresentation}{CT}
\bibcite{EtingofKazhdan:BialgebrasI}{EK}
\bibcite{Halacheva:Thesis}{Ha}
\bibcite{Kauffman:RotationalVirtualKnots}{Ka}
\bibcite{KirkLivingstonWang:Gassner}{KLW}
\bibcite{LeDimet:Gassner}{LD}
\bibcite{Wolfram:Mathematica}{Wo}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{15.01373pt}
\newlabel{tocindent1}{20.88867pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\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]{}
\citation{Alexander:TopologicalInvariants}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\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{brf}{\backcite{Alexander:TopologicalInvariants}{{1}{(document)}{Doc-Start}}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}}
\@writefile{brf}{\backcite{Self}{{1}{}{Doc-Start}}}
\citation{Alexander:TopologicalInvariants}
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces  A demo program computing $z_1$, some initial data, and a sample run on the 0-framed trefoil knot. The program is written in {\sl  Mathematica}\nonbreakingspace \cite  {Wolfram:Mathematica} and is available at\nonbreakingspace \cite  {Self}. \relax }}{2}{figure.caption.2}}
\@writefile{brf}{\backcite{Wolfram:Mathematica}{{2}{1.1}{figure.caption.2}}}
\@writefile{brf}{\backcite{Self}{{2}{1.1}{figure.caption.2}}}
\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
\newlabel{fig:Splash}{{1.1}{2}{A demo program computing $z_1$, some initial data, and a sample run on the 0-framed trefoil knot. The program is written in {\sl Mathematica}~\cite {Wolfram:Mathematica} and is available at~\cite {Self}. \relax }{figure.caption.2}{}}
\@writefile{brf}{\backcite{Alexander:TopologicalInvariants}{{2}{1}{theorem.1.1}}}
\citation{Bar-NatanSelmani:MetaMonoids}
\citation{KBH}
\citation{Halacheva:Thesis}
\citation{Archibald:Thesis}
\citation{LeDimet:Gassner}
\citation{KirkLivingstonWang:Gassner}
\citation{CimasoniTuraev:LagrangianRepresentation}
\citation{CimasoniConway:BurauAlexander}
\citation{Wolfram:Mathematica}
\citation{Self}
\citation{Wolfram:Mathematica}
\citation{Self}
\@writefile{brf}{\backcite{Bar-NatanSelmani:MetaMonoids, KBH}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{Halacheva:Thesis}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{Archibald:Thesis}{{3}{1}{theorem.1.1}}}
\@writefile{brf}{\backcite{LeDimet:Gassner, KirkLivingstonWang:Gassner, CimasoniTuraev:LagrangianRepresentation, CimasoniConway:BurauAlexander}{{3}{1}{theorem.1.1}}}
\pp@spagectr{FN@totalid}{5}{1}{3}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Algebras, Yang-Baxter Elements and Spinners, Invariants}}{3}{section.2}}
\newlabel{sec:generalities}{{2}{3}{Algebras, Yang-Baxter Elements and Spinners, Invariants}{section.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces  A demo program computing $z_0$, some initial data, and a sample run on the knot $8_{17}$. The program is written in {\sl  Mathematica}\nonbreakingspace \cite  {Wolfram:Mathematica} and is available at\nonbreakingspace \cite  {Self}. \relax }}{4}{figure.caption.3}}
\@writefile{brf}{\backcite{Wolfram:Mathematica}{{4}{3.1}{figure.caption.3}}}
\@writefile{brf}{\backcite{Self}{{4}{3.1}{figure.caption.3}}}
\newlabel{fig:Splash0}{{3.1}{4}{A demo program computing $z_0$, some initial data, and a sample run on the knot $8_{17}$. The program is written in {\sl Mathematica}~\cite {Wolfram:Mathematica} and is available at~\cite {Self}. \relax }{figure.caption.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{The Lie Algebra ${\mathfrak  g}_0$, the Invariant $z_0$, and the Alexander Polynomial}}{4}{section.3}}
\newlabel{sec:g0}{{3}{4}{The Lie Algebra $\frakg _0$, the Invariant $z_0$, and the Alexander Polynomial}{section.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The Lie Algebra ${\mathfrak  g}_1$ and the Invariant $z_1$}}{4}{section.4}}
\newlabel{sec:g1}{{4}{4}{The Lie Algebra $\frakg _1$ and the Invariant $z_1$}{section.4}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Computing $z_1$}}{4}{section.5}}
\newlabel{sec:z1}{{5}{4}{Computing $z_1$}{section.5}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{An Aside on Ribbon Knots}}{4}{section.6}}
\newlabel{sec:ribbon}{{6}{4}{An Aside on Ribbon Knots}{section.6}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Questions}}{4}{section.7}}
\newlabel{sec:questions}{{7}{4}{Questions}{section.7}{}}
\bibcite{Alexander:TopologicalInvariants}{Al}
\bibcite{Archibald:Thesis}{Ar}
\bibcite{Bar-Natan:OnVassiliev}{BN1}
\bibcite{KBH}{BN2}
\bibcite{Bar-NatanSelmani:MetaMonoids}{BNS}
\bibcite{Self}{BNVDV}
\bibcite{CimasoniConway:BurauAlexander}{CC}
\bibcite{CimasoniTuraev:LagrangianRepresentation}{CT}
\bibcite{EtingofKazhdan:BialgebrasI}{EK}
\bibcite{Halacheva:Thesis}{Ha}
\bibcite{Kauffman:RotationalVirtualKnots}{Ka}
\bibcite{KirkLivingstonWang:Gassner}{KLW}
\bibcite{LeDimet:Gassner}{LD}
\bibcite{Wolfram:Mathematica}{Wo}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{15.01373pt}
\newlabel{tocindent1}{20.88867pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{5}{section*.4}}