From c0f6b823fee72db898728ee655235fba0d93644c Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 1 Aug 2024 11:41:19 +0200
Subject: First try at sphere figures.

---
 topology.tex | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

(limited to 'topology.tex')

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.
-- 
cgit v1.2.3-70-g09d2

