Ich brauche dringend Hilfe, um dieses kommutative Diagramm ansehnlich zu gestalten. Ich habe buchstäblich wochenlang daran herumgebastelt und das ist das Beste, was ich habe.
Die einzige Unterdrückung, die ich akzeptieren könnte, ist der Austausch $H^{n-p}(F)$gegen eine Unterdrückung wie $\mathcal{F}$. Der Code lautet:
\[\begin{tikzpicture}[scale=1.5]
\node (sa) at (0,5) {$\ldots$};
\node (sb) at (4,5) {$\ldots$};
\node (a1) at (0,4.3) {$\mathop\bigoplus\limits_{p = 0}^n [H^p(U\cup V) \otimes H^{n-p}(F)]$};
\node (a2-1) at (-.12,3.3) {$\mathop\bigoplus\limits_{p = 0}^n [(H^p(U)\otimes H^{n-p}(F)$};
\node (a2-2) at (0,3) {$\oplus$};
\node (a2-3) at (.16,2.7) {$(H^p(V)\otimes H^{n-p}(F))]$};
\node (a3) at (0,1.7) {$\mathop\bigoplus\limits_{p = 0}^n [H^p(U\cap V)\otimes H^{n-p}(F)]$};
\node (a4) at (0,.7) {$\mathop\bigoplus\limits_{p = 0}^n [H^{p+1}(U\cup V) \otimes H^{n-p}(F)]$};
\node (b1) at (4,4.3) {$H^n(\pi^{-1}(U\cup V))$};
\node (b2-1) at (4,3.3) {$H^n(U\times F)$};
\node (b2-2) at (4,3) {$\oplus$};
\node (b2-3) at (4,2.7) {$H^n(V\times F)$};
\node (b3) at (4,1.7) {$H^n((U\cap V\times F))$};
\node (b4) at (4,.7) {$H^{n+1}(\pi^{-1}(U\cup V))$};
\node (ea) at (0,0) {$\ldots$};
\node (eb) at (4,0) {$\ldots$};
\path[->,font=\scriptsize,>=latex]
([xshift=5pt]sa.east) edge node[above]{$\Psi$} ([xshift=-5pt]sb.west)
(a1) edge node[above]{$\Psi$} (b1)
([xshift= 36pt]a2-2.east) edge node[above]{$\Psi$} ([xshift= -20pt]b2-2.west)
(a3) edge node[above]{$\Psi$} (b3)
([xshift=5pt]ea.east) edge node[above]{$\Psi$} ([xshift=-5pt]eb.west)
(a4) edge node[above]{$\Psi$} (b4)
(sa) edge ([yshift= -3.6pt]a1.north)
([yshift=5pt]a1.south) edge node[left]{$\delta$} ([xshift= 3.43pt,yshift=-4pt]a2-1.north)
([xshift= -4.55pt]a2-3.south) edge node[left]{$\gamma$} ([yshift=-3.6pt]a3.north)
([yshift= 5pt]a3.south) edge node[left]{$d^*$} ([yshift= -3.6pt]a4.north)
([yshift= 5pt]a4.south) edge (ea)
(sb) edge (b1)
(b1) edge node[right]{$\delta$} (b2-1)
(b2-3) edge node[right]{$\gamma$} (b3)
(b3) edge node[right]{$d^*$} (b4)
(b4) edge (eb);
\end{tikzpicture}\]
Antwort1
Hier ist eine Möglichkeit mit tikz-cd; die Psi-Beschriftungen wären jedoch besser ausgerichtet; dortsollenWeg sein!
\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{tikz-cd}
\begin{document}
\[
\newcommand{\sbop}{\mathop{\textstyle\bigoplus}\limits}
\begin{tikzcd}[column sep=6em,row sep=large]
\cdots \arrow[r,"\Psi"] \arrow[d] & \cdots \arrow[d]
\\
\smash{\sbop_{p = 0}^n}\, [H^p(U\cup V) \otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d,swap,"\delta"]
& H^n(\pi^{-1}(U\cup V)) \arrow[d,"\delta"]
\\
\begin{multlined}
\smash[t]{\sbop_{p = 0}^n}\, [(H^p(U)\otimes H^{n-p}(F) \\
\oplus (H^p(V)\otimes H^{n-p}(F))]
\end{multlined}
\arrow[r,"\Psi"] \arrow[d,swap,"\gamma"]
& H^n(U\times F) \oplus H^n(V\times F) \arrow[d,"\gamma"]
\\
\smash{\sbop_{p = 0}^n}\, [H^p(U\cap V)\otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d,swap,"d^*"]
& H^n((U\cap V\times F)) \arrow[d,"d^*"]
\\
\smash{\sbop_{p = 0}^n}\, [H^{p+1}(U\cup V) \otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d]
& H^{n+1}(\pi^{-1}(U\cup V)) \arrow[d]
\\
\cdots \arrow[r,"\Psi"] & \cdots
\end{tikzcd}
\]
\end{document}
