It is known that a complex orientation of a homology theory leads to a formal group law.

It is similar to the homology theory introduced rather sketchily by Kolmogorov in 1936.

Stratifolds can be used to construct new homology theories.

One can develop enough differential topology of stratifolds to show that these define a homology theory.

The left hand sides of these homomorphisms are homology theories evaluated at a point.

A similar construction, also introduced by Floer, provides a homology theory associated to three-dimensional manifolds.

A homology theory is formed from the vector space spanned by the critical points of this function.

The cobordism groups are the coefficient groups of a generalised homology theory.

These homology theories have contributed to further mainstreaming of knot theory.

An example is the complex defining the homology theory of a (finite) simplicial complex.