The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original simplicial homology. It is distinct from singular cohomology, which is obtained from the dual cochain complex.
Singular Homology
See also
Cochain Complex, Homology, Simplicial Homology, Singular CohomologyExplore with Wolfram|Alpha
References
Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Referenced on Wolfram|Alpha
Singular HomologyCite this as:
Weisstein, Eric W. "Singular Homology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SingularHomology.html