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\begin{document}
\parindent 0in

%\parbox[b]{4in}{
%  {\tiny Dror Bar-Natan: MAT 1350 Knot Theory: \LARGE\bf Tentative Plan}
%  }
\parbox[b]{1.5in}{\tiny
  \href{http://www.math.toronto.edu/~drorbn}{Dror Bar-Natan}: \href{http://www.math.toronto.edu/~drorbn/classes}{Classes}:
  \newline \href{http://www.math.toronto.edu/~drorbn/classes/\#2122}{2021-22}: \href{http://drorbn.net/21-1350}{MAT 1350 Knot Theory}:
}~{\LARGE\bf Homework Assignment 2}
\hfill\parbox[b]{2in}{\tiny
  \null\hfill\sheeturl
  \newline\null\hfill Due October 1 at midnight
}~%
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  \qrcode[height=1.2em,level=L,nolink]{drorbn.net/21-1350}
}~\parbox[b]{0.3in}{\tiny\href{http://www.math.toronto.edu/~drorbn/bv.html}{Better\newline vaxxed!}}

\vskip -3mm
\rule{\linewidth}{1pt}
\vskip 5mm

\begin{center}\begin{minipage}{6.5in}

\vskip 3mm{\bf Problem 1. } If the upper black is homeomorphic to the lower black, what's the image of red under this homeomorphism?

\[ \input{figs/3Camel.pdf_t} \]

\vskip 3mm{\bf Problem 2. } Prove that if the Gordian distance between the knots $K_1$ and $K_2$ is 1, then the difference between their genera is at most 1. Namely, that
\[ |g(K_1)-g(K_2)| \leq 1 \]
{\red Ouch! This is wrong! For example, the unknotting number of the knot $6_2$ is 1, but its genus is 2. Sorry.}

\vskip 3mm{\bf Problem 3. } Prove that a knot is ribbon iff for some $n>0$ there is a tangle $T$ with $2n$ strands whose skeleton is as in the figure below such that $\tau(T)$ is the untangle and $\kappa(T)=K$, where $\tau$ and $\kappa$ are defined by the figure below.
\[ \input{figs/taukappa.pdf_t} \]

\end{minipage}\end{center}

\end{document}


