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Commit 2c9071bc authored by Luke Naylor's avatar Luke Naylor
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Add alternative pdf strings for mathmode in section titles

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......@@ -190,7 +190,13 @@ For the next subsections, we consider $q$ to be fixed with one of these values,
and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
\subsection{$\Delta(E) + \Delta(G) \leq \Delta(F)$}
\subsection{
\texorpdfstring{
$\Delta(E) + \Delta(G) \leq \Delta(F)$
}{
Δ(E) + Δ(G) ≤ Δ(F)
}
}
\label{subsect-d-bound-bgmlv1}
This condition expressed in terms of $R,C,D,r,c,d$ looks as follows:
......@@ -300,7 +306,13 @@ In the case $\beta = \beta_{-}$ (or $\beta_{+}$) we have
$\chern^{\beta}_2(F) = 0$,
so some of these expressions simplify.
\subsection{$\Delta(E) \geq 0$}
\subsection{
\texorpdfstring{
$\Delta(E) \geq 0$
}{
Δ(E) ≥ 0
}
}
This condition expressed in terms of $R,C,D,r,c,d$ looks as follows:
......@@ -384,7 +396,13 @@ Notice that for $\beta = \beta_{-}$ (or $\beta_{+}$), that is when
$\chern^{\beta}_2(F)=0$, the constant and linear terms match up with the ones
for the bound found for $d$ in subsection \ref{subsect-d-bound-bgmlv1}.
\subsection{$\Delta(G) \geq 0$}
\subsection{
\texorpdfstring{
$\Delta(G) \geq 0$
}{
Δ(G) ≥ 0
}
}
\label{subsect-d-bound-bgmlv3}
This condition expressed in terms of $R,C,D,r,c,d$ looks as follows:
......@@ -516,14 +534,14 @@ $\chern^{\beta}_2(F) = 0$,
so some of these expressions simplify, and in particular, the constant and
linear terms match those of the other bounds in the previous subsections.
\subsection{Bounds on $r$}
\subsection{Bounds on \texorpdfstring{$r$}{r}}
Now, the inequalities from the last three subsections will be used to find, for
each given $q=\chern^{\beta}_1(E)$, how large $r$ needs to be in order to leave
no possible solutions for $d$. At that point, there are no Chern characters
$(r,c,d)$ that satisfy all inequalities to give a pseudowall.
\subsubsection{All circular walls left of vertical wall}
\subsubsection{All circular pseudowalls left of vertical wall}
Suppose we take $\beta = \beta_{-}$ in the previous subsections, to find all
circular walls to the left of the vertical wall (TODO as discussed in ref).
......
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