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For example, in page 353 of Ranicki's book Algebraic and geometric surgery,

there is a braid of long exact sequences like so:

enter image description here

I use xy-pic.

Thanks in advance!

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3  
@AndrewStacey is on his way :) –  percusse Oct 7 '13 at 11:53

3 Answers 3

up vote 10 down vote accepted

That brings back memories. But here is the basic structure. From the xy guide you will learn how to make the arrows curve more (if needed)

\documentclass[a4paper]{memoir}
\usepackage[all]{xy}
\usepackage{amsmath}
\begin{document}

\[
\xymatrix{
A \ar[rd] \ar@/^/[rr] &
&
C \ar[rd] \ar@/^/[rr] &
&
E \ar[rd] \ar@/^/[rr] &
&
G \\
&
B \ar[ur] \ar[dr] &
&
D \ar[ur] \ar[dr]&
&
F \ar[ur] \ar[dr]&
\\
A \ar[ur] \ar@/_/[rr]^J &
&
C \ar[ur] \ar@/_/[rr]^{\sigma_*} &
&
E \ar[ur] \ar@/_/[rr] &
&
G \\
}
\]

\end{document}

enter image description here

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Decreasing the row spacing may help: \xymatrix@R-1pc{... or so. –  egreg Oct 7 '13 at 12:25

Remarks

The same as @daleif's answer, just with tikz-cd instead of xy-pic. Have fun!

Implementation

\documentclass[tikz]{standalone}
\usepackage{amsmath,amssymb,tikz-cd}
\begin{document}
\begin{tikzcd}[cells={nodes={minimum width=1.5cm}}]% to make it more symmetric
    L_{m+1}(\mathbb{Z}) \arrow[bend left]{rr} \arrow{rd}
    &
    & \Theta_m \arrow[bend left]{rr}{0} \arrow{rd}
    &
    & \pi_m(BO) \arrow[bend left]{rr} \arrow{rd}
    &
    & \Omega^{fr}_{m-1}
    \\
%
    & \Theta^{fr}_{m} \arrow{ru} \arrow{rd}
    &
    & A_m \arrow{ru} \arrow{rd}
    &
    & \Theta^{fr}_{m-1} \arrow{ru} \arrow{rd}
    &
    \\
%
    \pi_m(O) \arrow[bend right]{rr}{J} \arrow{ru}
    &
    & \Omega^{fr}_m \arrow[bend right]{rr}{\sigma^*} \arrow{ru}
    &
    & L_m(\mathbb{Z}) \arrow[bend right]{rr} \arrow{ru}
    &
    & \Theta_{m-1}
\end{tikzcd}
\end{document}

Output

enter image description here

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much nicer arrowheads ;-) –  daleif Oct 8 '13 at 11:48
    
@daleif tikz-cd (and tikz as well) automatically uses the arrowhead of the standard Computer Modern \rightarrow, to match the equations. You can still customize the arrowheads by adding /tikz/commutative diagrams/diagrams={>=*<arrow head>*} to either \tikzset or to the parameters of the drawing. –  Henri Menke Oct 8 '13 at 11:54
    
@daleif -- if you choose the option [cmtip] for xy you'll get the "nicer" arrowheads. not sure why, but [all] doesn't do it. –  barbara beeton Oct 8 '13 at 13:44

Another tikz option, but using matrix of nodes.

screenshot

% arara: pdflatex
\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{matrix}
\usepackage{amssymb}

% make the arrows look like stealth fighter jets
\tikzset{>=stealth}
\begin{document}

\begin{tikzpicture}

    \matrix[name=M, matrix of nodes,cells={nodes={minimum width=1.5cm}}, column sep=1.5cm, row sep=1cm]{
        $L_{m+1}(\mathbb{Z})$ &                & $\Theta_m$      &       & $\pi_m(BO)$       &                    & $\Omega_{m-1}^{fr}$ \\
                              &$\Theta_m^{fr}$ &                 & $A_m$ &                   & $\Theta_{m-1}^{fr}$& \\ 
        $\pi_m(O)$            &                & $\Omega_m^{fr}$ &       & $L_m(\mathbb{Z})$ &                    & $\Theta_{m-1}$ \\
    };
    % straight edges
    \foreach \start/\end in {
        M-1-1/M-2-2,
        M-3-1/M-2-2,
        M-2-2/M-1-3,
        M-2-2/M-3-3,
        M-1-3/M-2-4,
        M-3-3/M-2-4,
        M-2-4/M-1-5,
        M-2-4/M-3-5,
        M-1-5/M-2-6,
        M-3-5/M-2-6,
        M-2-6/M-1-7,
    M-2-6/M-3-7}
    {
        \draw[->] (\start) edge (\end);
    }
    % curved arrows
    \draw[->] (M-1-1) to[out=30,in=150] (M-1-3);
    \draw[->] (M-1-3) to[out=30,in=150] node[pos=0.5,above]{$0$} (M-1-5);
    \draw[->] (M-1-5) to[out=30,in=150]  (M-1-7);
    \draw[->] (M-3-1) to[out=-30,in=-150] node[pos=0.5,above]{$J$} (M-3-3);
    \draw[->] (M-3-3) to[out=-30,in=-150] node[pos=0.5,above]{$\sigma^*$} (M-3-5);
    \draw[->] (M-3-5) to[out=-30,in=-150] (M-3-7);
\end{tikzpicture}

\end{document}
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