nLab chain




In homology theory

In homology/homological algebra, 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.

In de Rham cohomology, a de Rham chain? is a formal linear combination of parametrized submanifolds? with boundary.

In order theory

In order theory, a chain is a totally ordered subset of a given poset (or proset). See also antichain

For applications of this concept see for instance

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

Last revised on December 4, 2022 at 07:49:46. See the history of this page for a list of all contributions to it.