A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is considered to be homologous to zero if it is the boundary of something having dimension one greater. For instance, two points that can be connected by a path comprise the boundary for that path, so any two points in a component are homologous and represent the same homology class.
SEE ALSO:Cohomology, Cohomology Class, Homology, Homology Group, Homology Intersection
This entry contributed by Todd Rowland
