# Contents

## Idea

Generally, a chain is an element of a chain complex.

Specifically for the complex computing the singular homology of a topological space, a singular chain is a formal linear combination of simplices in that space.

$H_n = Z_n/B_n$(chain-)homology(cochain-)cohomology$H^n = Z^n/B^n$
$C_n$chaincochain$C^n$
$Z_n \subset C_n$cyclecocycle$Z^n \subset C^n$
$B_n \subset C_n$boundarycoboundary$B^n \subset C^n$

Created on August 27, 2012 00:39:28 by Urs Schreiber (89.204.139.66)