File:Mayer-Vietoris naturality.png

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Summary

DescriptionMayer-Vietoris naturality.png	English: A commutative diagram of long exact sequences (Mayer-Vietoris sequences).
Date	16 December 2008
Source	Own work
Author	GeometryGirl
Other versions	${\begin{matrix}\cdots &H_{n+1}(X_{1})&\to &H_{n}(A_{1}\cap B_{1})&\to &H_{n}(A_{1})\oplus H_{n}(B_{1})&\to &H_{n}(X_{1})&\to &H_{n-1}(A_{1}\cap B_{1})&\to &\cdots \\&f_{}{\Bigg \downarrow }&&f_{}{\Bigg \downarrow }&&f_{}{\Bigg \downarrow }&&f_{}{\Bigg \downarrow }&&f_{*}{\Bigg \downarrow }\\\cdots &H_{n+1}(X_{2})&\to &H_{n}(A_{2}\cap B_{2})&\to &H_{n}(A_{2})\oplus H_{n}(B_{2})&\to &H_{n}(X_{2})&\to &H_{n-1}(A_{2}\cap B_{2})&\to &\cdots \\\end{matrix}}$

Data file

The commutative diagram was done using the following LaTeX code:

\documentclass[12]{article}

\usepackage[left=1cm,top=2cm,right=2cm,nohead]{geometry}
\usepackage{amsmath,amscd} 

\begin{document}

\[\minCDarrowwidth13pt
\begin{CD}
\cdots@>>>H_{n+1}(X_1) @>>> H_n(A_1\cap B_1) @>>> H_n(A_1)\oplus H_n(B_1)@>>>H_n(X_1)@>>>H_{n-1}(A_1\cap B_1)@>>>\cdots\\ 
@.@Vf_*VV@Vf_*VV@Vf_*VV@Vf_*VV@Vf_*VV@.\\
\cdots@>>>H_{n+1}(X_2) @>>> H_n(A_2\cap B_2) @>>> H_n(A_2)\oplus H_n(B_2)@>>>H_n(X_2)@>>>H_{n-1}(A_2\cap B_2)@>>>\cdots\\ 
\end{CD}
\]

\end{document}

Licensing

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File history

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	Date/Time	Dimensions	User	Comment
current	14:42, 5 January 2009	1,435 × 196 (31 KB)	GeometryGirl	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	11:07, 5 January 2009	1,361 × 196 (27 KB)	GeometryGirl	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	11:58, 23 December 2008	1,343 × 147 (24 KB)	GeometryGirl	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	16:21, 16 December 2008	1,156 × 130 (21 KB)	GeometryGirl	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	16:17, 16 December 2008	550 × 73 (12 KB)	GeometryGirl
	16:13, 16 December 2008	561 × 71 (13 KB)	GeometryGirl	{{Information \|Description={{en\|1=A commutative diagram of long exact sequences (Mayer-Vietoris sequences).}} \|Source=Own work by uploader \|Author=GeometryGirl \|Date=16/12/08 \|Permission= \|other_versions= }} <!--{{ImageUpload\|full}}