The proof of the uniqueness theorem of the first talk begins with a geometric representation of an ordinary singular cycle by an embedded manifold with singularities in the sense of stratified spaces. Let us call these varieties. One also uses a representation of an ordinary singular homology by an embedded variety with boundary.

There are many examples of generalised homology theories that can be defined by mappings from varieties with specific kinds of singularities. Angle assignments to these cycles leads to extraordinary differential cohomology theory.

As an example we have such a geometric cycle approach to differential K theory. The approach of the first talk and this approach can be compared using the eta invariant theory of Atiyah,Patodi, and Singer.

Lecture #13412

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