Chain (algebraic topology)

This article is about algebraic topology. For the term chain in order theory, see chain (order theory).

In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations of k-simplices (respectively, k-cubes),[1][2][3] but not necessarily connected. Chains are used in homology; the elements of a homology group are equivalence classes of chains.

  1. ^ Hatcher, Allen (2002). Algebraic Topology. Cambridge University Press. ISBN 0-521-79540-0.
  2. ^ Lee, John M. (2011). Introduction to topological manifolds (2nd ed.). New York: Springer. ISBN 978-1441979391. OCLC 697506452.
  3. ^ Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian (2004). Computational homology. Applied Mathematical Sciences. Vol. 157. New York: Springer-Verlag. doi:10.1007/b97315. ISBN 0-387-40853-3. MR 2028588.