  We overview recent results on the mathematical foundations of Cutkosky rules.
We emphasize that the two operations of shrinking an internal edge or putting
internal lines on the mass-shell are natural operation on the cubical chain
complex studied in the context of geometric group theory. This together with
Cutkosky's theorem regarded as a theorem which informs us about variations
connected to the monodromy of Feynman amplitudes allows for a systematic
approach to normal and anomalous thresholds, dispersion relations and the
optical theorem. In this report we follow [1] closely.
