diff --git a/main.tex b/main.tex index 727da0b4fb21298ea58680d313e8141c72a97116..f73822987e690704c35d31f3547cbec429a49b8f 100644 --- a/main.tex +++ b/main.tex @@ -56,6 +56,16 @@ $0 \leq \chern^\beta_1(E) \leq \chern^\beta_1(F)$. Finally, there's a condition ensuring that the radius of the circular wall is strictly positive: $\chern^\beta_2(E) > 0$. +For any fixed $\chern_0(E)$, the inequality +$0 \leq \chern^{\beta_{-}}_1(E) \leq \chern^{\beta_{-}}_1(F)$, +allows us to bound $\chern_1(E)$. Then, the other inequalities allow us to +bound $\chern_2(E)$. The final part to showing the finiteness of pseudowalls +would be bounding $\chern_0(E)$. This has been hinted at in [ref] and done +explicitly by Benjamin Schmidt within a computer program which computes +pseudowalls. Here we discuss these bounds in more detail, along with the methods +used, followed by refinements on them which give explicit formulae for tighter +bounds on $\chern_0(E)$ of potential destabilizers $E$ of $F$. + \section{Section 1}