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.
Singular Homology
See also
Homology, Simplicial HomologyExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Singular Homology." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SingularHomology.html