First try at sphere figures.

3 files changed, 17 insertions, 0 deletions

diff --git a/figs/connected.pdf b/figs/connected.pdf
new file mode 100644
index 0000000..8fccdaf
--- /dev/null
+++ b/figs/connected.pdf
diff --git a/figs/shattered.pdf b/figs/shattered.pdf
new file mode 100644
index 0000000..d3d2957
--- /dev/null
+++ b/figs/shattered.pdf
diff --git a/topology.tex b/topology.tex
index 8c21ee9..58e341a 100644
--- a/topology.tex
+++ b/topology.tex
@@ -139,6 +139,23 @@ $\mathbb M(1)=\frac1N\phi(1)\cdot\mathbf x_0$, the result is
   \end{aligned}
 \end{equation}
 
+\begin{figure}
+  \includegraphics[width=0.49\columnwidth]{figs/connected.pdf}
+  \hfill
+  \includegraphics[width=0.49\columnwidth]{figs/shattered.pdf}
+
+  \caption{
+    Cartoon of the topology of the CCSP solution manifold implied by our
+    calculation. The arrow shows the vector $\mathbf x_0$ defining the height
+    function. The region of solutions is shaded orange, and the critical points
+    of the height function restricted to this region are marked with a red
+    point. For $\alpha<1$, there are few simply connected regions with most of
+    the minima and maxima contributing to the Euler characteristic concentrated
+    at the height $m_\mathrm a^*$. For $\alpha\geq1$, there are many simply
+    connected regions and most of their minima and maxima are concentrated at
+    the equator.
+  }
+\end{figure}
 
 \begin{acknowledgements}
   JK-D is supported by a \textsc{DynSysMath} Specific Initiative of the INFN.