nLab
chain

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 nH_n = Z_n/B_n(chain-)homology(cochain-)cohomologyH n=Z n/B nH^n = Z^n/B^n
C nC_nchaincochainC nC^n
Z nC nZ_n \subset C_ncyclecocycleZ nC nZ^n \subset C^n
B nC nB_n \subset C_nboundarycoboundaryB nC nB^n \subset C^n

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