Relative homology

The homology groups (cf. Homology group) of a pair of spaces . They are defined by the quotient complex of the chain complex with coefficients in a group by the subcomplex consisting of all chains with support in . These groups are usually not altered by "excisionexcision" , i.e. by the replacement of the pair by a pair , where is an open subset of contained in . The relative cohomology groups are defined by the subcomplex of the chain complex consisting of all cochains with support in , while the quotient complex usually defines cohomology groups of the subset .

References

[1]	E.G. Sklyarenko, "Homology and cohomology of general spaces" , Springer (Forthcoming) (Translated from Russian)

References

[a1]	E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966)
[a2]	R.M. Switzer, "Algebraic topology - homotopy and homology" , Springer (1975) pp. 360ff