diff --git a/main.pdf b/main.pdf index 9310d50..b722adf 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index d0a2196..a01d670 100644 --- a/main.tex +++ b/main.tex @@ -22,9 +22,9 @@ \DeclareMathOperator{\lensop}{L} \DeclareMathOperator{\rotmatop}{R} \DeclareMathOperator{\soop}{SO} -\newcommand*{\lens}[2]{\lensop\left(#1,#2\right)} % +\newcommand*{\lens}[2]{\textcolor{darkyellow}{\lensop\left(\textcolor{black}{#1},\textcolor{black}{#2}\right)}} % \newcommand*{\so}[1]{\soop\left(#1\right)} -\newcommand*{\rotmat}[1]{\rotmatop\left(#1\right)} +\newcommand*{\rotmat}[1]{\textcolor{red}{\rotmatop\left(\textcolor{black}{#1}\right)}} \renewcommand{\S}{\mathbb{S}} \newcommand{\R}{\mathbb{R}} @@ -63,6 +63,7 @@ code-for-last-col = \color{blue} \setbeamercolor{titlebox}{fg=black,bg=white} \definecolor{silver}{RGB}{192, 192, 192} +\definecolor{darkyellow}{RGB}{186, 142, 35} \begin{document} @@ -136,14 +137,13 @@ code-for-last-col = \color{blue} \begin{frame}{Inhomogeneous spherical space} \begin{itemize} - \item Manifolds of the form $\S^3/\Gamma$ with $\Gamma$ a group acting on $\S^3$. \item Multi-connected space: it has non-contractable loops. \item Inhomogeneous space: it does not look identical from every point in space. \pause \item Fixing $|\Gamma|=8$, we have three multi-connected manifolds, up to equivalence: \pause \begin{enumerate} - \item homogeneous: $N3$ and $L(8,1)$. - \item inhomogeneous: $N2 \equiv L(8,3)$. + \item homogeneous: $N3$ and $\lens 8 1 $. + \item inhomogeneous: $N2 \equiv \lens 8 3 $. \end{enumerate} \pause \item Results: inhomogeneous spaces have more variety in the CMB anisotropies than homogeneous spaces, because the strength of anisotropy suppression is observer dependent.