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Homology (mathematics)
In
mathematics
(especially
algebraic topology
and
abstract algebra
),
homology
(in part from
Greek
ὁμός
homos
"identical") is a general way of associating a sequence of algebraic objects such as
abelian groups
or
module
s to other mathematical objects such as
topological spaces
. Homology groups were originally defined in
algebraic topology
. However, similar constructions are available in a wide variety of other contexts, such as
group
s,
Lie algebras
,
Galois theory
, and
algebraic geometry
.
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